Homotopy theory and duality

by Peter John Hilton

Publisher: Nelson in London

Written in English
Published: Pages: 224 Downloads: 400
Share This

Subjects:

  • Homotopy theory.,
  • Duality theory (Mathematics)

Edition Notes

Bibliography: p. 219-221.

Statementby Peter Hilton.
SeriesNotes on mathematics and its applications
Classifications
LC ClassificationsQA611 .H644 1967
The Physical Object
Paginationx, 224 p.
Number of Pages224
ID Numbers
Open LibraryOL4355328M
LC Control Number78397522

reader, and since readability is one of the first priorities of the book, this homotopic interpretation of homology and cohomology is described only after the latter theories have been developed independently of homotopy theory. Preceding the four main chapters there is a preliminary Chapter 0 introducing. Aug 27,  · There are a ton of relationships. Let me touch on two. Motivic homotopy theory is one such relationship: this is supposed to be the “homotopy theory of schemes”. (Mike Hopkins has a nice lecture here: Michael Hopkins - Algebraic and motivic vector. Homotopy, homotopy equivalence, the categories of based and unbased space. Week 2. Higher homotopy groups, weak homotopy equivalence, CW complex. Week 3. Cofibrations and the Homotopy Extension Property. Week 4. Relative homotopy groups, homotopy fiber, long exact sequence in homotopy, Whitehead theorem. Week 5. Cellular and CW approximation. Book Description: This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry.

A distinguishing feature is a thematic focus on Eckmann-Hilton duality. this book offers an attractive option for a course or self-study, fitting a niche between the introductory texts of Munkres, Massey and Thatcher and the comprehensive treatments of homotopy theory by Spanier and walkingshops.com: Martin Arkowitz. (P. Goerss) Gross-Hopkins duality. Brown-Comenetz duality and its variants are something of a curiosity in stable homotopy theory, but it is an insight of Hopkins that in the K (n)-local category it is much more like Serre-Grothendieck duality. Flesh out that statement. and analysis: homotopy theories are everywhere, along with functorial methods of relating them. This book is, however, not quite so cosmological in scope. The theory has broad applications in many areas, but it has always been quite a sharp tool within ordinary . Key words and phrases. ex-space, parametrized spectrum, parametrized homotopy theory, equivariant homotopy theory, parametrized stable homotopy theory, equivariant stable homotopy theory, transfer, twisted K-theory, Poincar´e duality, Atiyah duality, Thom spectrum, bicategory, model category May was partially supported by the NSF.

7 Homotopy Theory of Fibrations 9 Poincar e Duality, Intersection theory, and Linking numbers Poincar e Duality, the \shriek map", and the Thom isomorphism Duality The subject of much of this book is the topology of manifolds. n-dimensional. Ambidexterity in K(n)-Local Stable Homotopy Theory. Joint with Mike Hopkins. Investigates some surprising duality phenomena in the world of K(n)-local homotopy theory. Mostly finished, though it is a bit rough in places. Last update: December pdf: Representability Theorems. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces. Algebraic topology in general and homotopy theory in particular is in an exciting period of growth and transformation, driven in part by strong interactions with algebraic geometry, mathematical.

Homotopy theory and duality by Peter John Hilton Download PDF EPUB FB2

Homotopy theory and duality by Hilton, Peter and a great selection of related books, art and collectibles available now at walkingshops.com Homotopy Theory and Duality [P.J., Hilton] on walkingshops.com *FREE* shipping on qualifying offers.

Shipped from UK, please allow 10 to 21 business days for arrival. Good, ex. lib. Dust wrapper has tear at top of spineAuthor: Hilton, P.J.

Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study.

The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied. Introduction to Homotopy Theory is presented in nine chapters, taking the reader from ‘basic homotopy’ to obstruction theory with a lot of marvelous material in between.

Arkowitz’ book is a valuable text and promises to figure prominently in the education of many young topologists.” (Michael Berg, The Mathematical Association of Cited by: Introduction to Homotopy Theory is presented in Homotopy theory and duality book chapters, taking the reader from ‘basic homotopy’ to obstruction theory with a lot of marvelous material in between.

Arkowitz’ book is a valuable text and promises to figure prominently in the education of many young topologists.” Homotopy theory and duality book Berg, The Mathematical Association of.

The theory is also referred to as S-duality, but this can now cause possible confusion with the S-duality of string theory. It is named for Edwin Spanier and J. Whitehead, who developed it in papers from The basic point is that sphere complements determine the homology, but not the homotopy type, in.

About the book. Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between homotopy theory and type theory. In homotopy type theory, however, there may be multiple different paths =, and transporting an object along two different paths will yield two different results.

Therefore, in homotopy type theory, when applying the substitution property, it is necessary to state which path is being used. DUALITY IN HOMOTOPY THEORY With E. SPANIER Received November 29, 1.

Introduction. Certain results ([7], [8], [10], [11]) suggest t h a t there should be some principle of duality in homotopy theory.

Among other things one is led to expect that cohomotopy groups will appear as dual t Cited by: 1. As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems.

Some acquaintance with. The book can be used as a text for the second semester of an algebraic topology course. The intended audience of this book is advanced undergraduate or graduate students. The book could also be used by anyone with a little background in topology who wishes to learn some homotopy theory.

Oct 19,  · Another noteworthy pedagogical fact about Introduction to Homotopy Theory is the author’s choice to base much of his development on Eckmann-Hilton duality theory.

Says Arkowitz, “The Eckmann-Hilton theory has been around for about fifty years but there appears to be no book-length exposition of it, apart from the early lecture notes of.

Equivariant Stable Homotopy Theory. Authors; L. Gaunce Lewis Jr. Peter May; Mark Steinberger; Book. Citations; k Downloads; Part of the Lecture Notes in Mathematics book series (LNM, volume ) Log in to check access. Buy eBook. USD Instant download Homotopy duality homology homotopy theory.

Bibliographic information. DOI. Notes for a second-year graduate course in advanced topology at MIT, designed to introduce the student to some of the important concepts of homotopy theory.

This book consists of notes for a second year graduate course in advanced topology given by Professor Whitehead at M.I.T. Presupposing a knowledge of the fundamental group and of algebraic topology as far as singular theory, it is designed.

Jan 19,  · Elements of Homotopy Theory book. Read reviews from world’s largest community for readers. As the title suggests, this book is concerned with the element Elements of Homotopy Theory book.

Read reviews from world’s largest community for readers. Some acquaintance with manifolds and Poincare duality is desirable, but not essential.5/5(2). DUALITY IN RELATIVE HOMOTOPY THEORY With E. SPANIER* Received June 3, 1. Introduction In this paper we extend the duality introduced in [7] from the category of finite polyhedra to the category of finite polyhedral lattices and S-maps between them, restricted by carriers [6] which are join-homomorphisms (i.e.

Al U A2 - Bl U B.z if At -> Bt).Author: E.H. Spanier. Arkowitz’ book is a valuable text and promises to figure prominently in the education of many young topologists.” (Michael Berg, The Mathematical Association of America, October, ) From the Back Cover. This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology.4/5(3).

Mar 20,  · Homotopy Type Theory refers to a new field of study relating Martin-Löf’s system of intensional, constructive type theory with abstract homotopy theory. Propositional equality is interpreted as homotopy and type isomorphism as homotopy equivalence.

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint.

The presentation of the homotopy theory and the account of duality in homology manifolds make the text ideal for a course on either homotopy or homology walkingshops.com idea of 5/5(2). Why not a Roadmap for Homotopy Theory and Spectra. Ask Question Asked 6 years, 2 months ago.

Active 6 years, 2 months ago. All these references contain phrasing in terms of model categories, which seem indispensible to modern homotopy theory. Good references are Hovey's book and Hirschhorn's book.

The underlying theme of the entire book is the Eckmann-Hilton duality theory. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows:Brand: Martin Arkowitz. Apr 17,  · The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology.

Accord ingly, we move primarily in the realm of smooth manifolds and use the de Rham theory as a prototype of all of cohomology. For applications to homotopy theory we also discuss by way of analogy cohomology with arbitrary coefficients.

another on Goodwillie calculus. But in the book that emerged it seemed thematically appropriate to draw the line at stable homotopy theory, so space and thematic consistency drove these chapters to the cutting room floor. Problems and Exercises.

Many authors of textbooks assert that the only way to learn the subject is to do the exercises. Oct 19,  · Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory.

This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The book [Jam99] gives a treatment of the history of topology, while the chap-ter of May [May99b] (50 pages) covers stable homotopy theory from to Since then, the pace of development and publication has only quickened, a thorough history of stable homotopy theory would be a book by itself.

DOI link for Handbook of Homotopy Theory. Handbook of Homotopy Theory book. Handbook of Homotopy Theory. DOI link for Handbook of Homotopy Theory. Handbook of Homotopy Theory book. Edited By Haynes Miller. Edition 1st Edition. First Published eBook Published 23 January Pub.

location New York. Homotopy Theory of Higher Categories; Homotopy Theory of Higher Categories. mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories.

Another model for the homotopy theory of homotopy theories. Preprint Cited by: The Hardcover of the Elements of Homotopy Theory by George W. Whitehead at Barnes & Noble. FREE Shipping on $35 or more. this book is concerned with the elementary portion of the subject of homotopy theory.

It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal. The Mock Homotopy Category of Projectives and Grothendieck Duality Daniel Murfet September mock homotopy category of projectives, that extends the derived category of quasi-coherent can deduce from Grothendieck’s theory of duality that these two extensions of the derived category are equivalent.

First, a brief reminder about. This book explains the following topics: the fundamental group, covering spaces, ordinary homology and cohomology in its singular, cellular, axiomatic, and represented versions, higher homotopy groups and the Hurewicz theorem, basic homotopy theory including fibrations and cofibrations, Poincare duality for manifolds and manifolds with boundary.

Sep 11,  · This book collects in one place the material that a researcher in algebraic topology must know.the fundamental group, homological algebra, singular and cellular homology, and Poincaré duality.

Part II covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets.Introduction to Homotopy Theory / Edition 1. by Paul the fundamental group, homological algebra, singular and cellular homology, and Poincare duality.

Part II covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, spectral Price: $This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner.

It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding.