## see also

**K-theory** (7)

## e-books in Algebraic Topology category

**Residues and Duality**

by

**Robin Hartshorne**-

**Springer**,

**1966**

The main purpose of these notes is to prove a duality theorem for cohomology of quasi-coherent sheaves, with respect to a proper morphism of locally noetherian preschemes. Various such theorems are already known. Typical is the duality theorem ...

(

**934**views)

**An Elementary Illustrated Introduction to Simplicial Sets**

by

**Greg Friedman**-

**arXiv.org**,

**2016**

This is an introduction to simplicial sets and simplicial homotopy theory with a focus on the combinatorial aspects of the theory and their geometric/topological origins. Accessible to students familiar with the fundamentals of algebraic topology.

(

**3871**views)

**Topological Groups: Yesterday, Today, Tomorrow**

by

**Sidney A. Morris (ed.)**-

**MDPI AG**,

**2016**

The aim of this book is to describe significant topics in topological group theory in the early 21st century as well as providing some guidance to the future directions topological group theory might take by including some interesting open questions.

(

**2020**views)

**Modern Algebraic Topology**

by

**D. G. Bourgin**-

**Macmillan**,

**1963**

Contents: Preliminary algebraic background; Chain relationships; The absolute homology groups and basic examples; Relative omology modules; Manifolds and fixed cells; Omology exact sequences; Simplicial methods and inverse and direct limits; etc.

(

**3032**views)

**Differential Forms and Cohomology: Course**

by

**Peter Saveliev**-

**Intelligent Perception**,

**2013**

Differential forms provide a modern view of calculus. They also give you a start with algebraic topology in the sense that one can extract topological information about a manifold from its space of differential forms. It is called cohomology.

(

**3477**views)

**Topology Illustrated**

by

**Peter Saveliev**-

**Intelligent Perception**,

**2014**

The text follows the content of a fairly typical, two-semester, first course in topology. Some of the topics are: the shape of the universe, configuration spaces, digital image analysis, data analysis, social choice, and, of course, calculus.

(

**4475**views)

**Lectures on Introduction to Algebraic Topology**

by

**G. de Rham**-

**Tata Institute of Fundamental Research**,

**1969**

These notes were intended as a first introduction to algebraic Topology. Contents: Definition and general properties of the fundamental group; Free products of groups and their quotients; On calculation of fundamental groups; and more.

(

**5356**views)

**Algebraic and Geometric Surgery**

by

**Andrew Ranicki**-

**Oxford University Press**,

**2002**

Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more. This book aims to be an entry point to surgery theory for a reader who already has some background in topology.

(

**5543**views)

**Topology of Stratified Spaces**

by

**Greg Friedman, et al.**-

**Cambridge University Press**,

**2011**

This book concerns the study of singular spaces using techniques of geometry and topology and interactions among them. The authors cover intersection homology, L2 cohomology and differential operators, the topology of algebraic varieties, etc.

(

**4849**views)

**Manifold Theory**

by

**Peter Petersen**-

**UCLA**,

**2010**

These notes are a supplement to a first year graduate course in manifold theory. These are the topics covered: Manifolds (Smooth Manifolds, Projective Space, Matrix Spaces); Basic Tensor Analysis; Basic Cohomology Theory; Characteristic Classes.

(

**5287**views)

**Introduction to Algebraic Topology and Algebraic Geometry**

by

**U. Bruzzo**,

**2008**

Introduction to algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for algebraically integrable systems and the geometry of quantum field and string theory.

(

**6454**views)

**Higher Topos Theory**

by

**Jacob Lurie**-

**Princeton University Press**,

**2009**

Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.

(

**7507**views)

**Notes on the course Algebraic Topology**

by

**Boris Botvinnik**-

**University of Oregon**,

**2010**

Contents: Important examples of topological spaces; Constructions; Homotopy and homotopy equivalence; CW-complexes and homotopy; Fundamental group; Covering spaces; Higher homotopy groups; Fiber bundles; Suspension Theorem and Whitehead product; etc.

(

**5656**views)

**Introduction to Topological Groups**

by

**Dikran Dikranjan**-

**UCM**,

**2007**

These notes provide a brief introduction to topological groups with a special emphasis on Pontryaginvan Kampen's duality theorem for locally compact abelian groups. We give a completely self-contained elementary proof of the theorem.

(

**6240**views)

**Geometry of 2D Topological Field Theories**

by

**Boris Dubrovin**-

**arXiv**,

**1994**

These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Topics: WDVV equations and Frobenius manifolds; Polynomial solutions of WDVV; Symmetries of WDVV; etc.

(

**7834**views)

**A Primer on Homotopy Colimits**

by

**Daniel Dugger**-

**University of Oregon**,

**2008**

This is an expository paper on homotopy colimits and homotopy limits. These are constructions which should arguably be in the toolkit of every modern algebraic topologist. Many proofs are avoided, or perhaps just sketched.

(

**5322**views)

**A Topology Primer**

by

**Klaus Wirthmüller**-

**Technische Universität Kaiserslautern**,

**2002**

The purpose of this text is to make familiar with the basics of topology, to give a concise introduction to homotopy, and to make students familiar with homology. Readers are expected to have knowledge of analysis and linear algebra.

(

**8070**views)

**Lecture Notes on Motivic Cohomology**

by

**Carlo Mazza, Vladimir Voevodsky, Charles Weibel**-

**AMS**,

**2005**

This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings.

(

**5559**views)

**Topics in topology: The signature theorem and some of its applications**

by

**Liviu I. Nicolaescu**-

**University of Notre Dame**,

**2008**

The author discusses several exciting topological developments which radically changed the way we think about many issues. Topics covered: Poincare duality, Thom isomorphism, Euler, Chern and Pontryagin classes, cobordisms groups, signature formula.

(

**5666**views)

**Prerequisites in Algebraic Topology**

by

**Bjorn Ian Dundas**-

**NTNU**,

**2005**

This is not an introductory textbook in algebraic topology, these notes attempt to give an overview of the parts of algebraic topology, and in particular homotopy theory, which are needed in order to appreciate that side of motivic homotopy theory.

(

**6345**views)

**Homotopy Theories and Model Categories**

by

**W. G. Dwyer, J. Spalinski**-

**University of Notre Dame**,

**1995**

This paper is an introduction to the theory of model categories. The prerequisites needed for understanding this text are some familiarity with CW-complexes, chain complexes, and the basic terminology associated with categories.

(

**5388**views)

**The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres**

by

**Paul Goerss**-

**Northwestern University**,

**2007**

Contents: The Adams spectral sequence; Classical calculations; The Adams-Novikov Spectral Sequence; Complex oriented homology theories; The height filtration; The chromatic decomposition; Change of rings; The Morava stabilizer group.

(

**7831**views)

**Topology Lecture Notes**

by

**Thomas Ward**-

**UEA**,

**2001**

Contents: Topological and Metric Spaces, Homotopy Exquivalence, Fundamental Groups, Covering Spaces and Applications, Classification of Surfaces, Simplicial Complexes and Homology Groups, Homology Calculations, Simplicial Approximation, etc.

(

**7306**views)

**An Introduction to Algebraic Surgery**

by

**Andrew Ranicki**-

**arXiv**,

**2000**

Browder-Novikov-Sullivan-Wall surgery theory investigates the homotopy types of manifolds, using a combination of algebra and topology. It is the aim of these notes to provide an introduction to the more algebraic aspects of the theory.

(

**6469**views)

**scl**

by

**Danny Calegari**-

**Mathematical Society of Japan**,

**2009**

This is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric group theory, bounded cohomology, symplectic topology.

(

**5702**views)

**Lectures on Etale Cohomology**

by

**J. S. Milne**,

**2008**

These are the notes for a course taught at the University of Michigan in 1989 and 1998. The emphasis is on heuristic arguments rather than formal proofs and on varieties rather than schemes. The notes also discuss the proof of the Weil conjectures.

(

**5347**views)

**Equivariant Stable Homotopy Theory**

by

**G. Jr. Lewis, J. P. May, M. Steinberger, J. E. McClure**-

**Springer**,

**1986**

Our purpose is to establish the foundations of equivariant stable homotopy theory. We shall construct a stable homotopy category of G-spectra,and use it to study equivariant duality, equivariant transfer, the Burnside ring, and related topics.

(

**9585**views)

**H Ring Spectra and Their Applications**

by

**R. R. Bruner, J. P. May, J. E. McClure, M. Steinberger**-

**Springer**,

**1986**

This volume concerns spectra with enriched multiplicative structure. It is a truism that interesting cohomology theories are represented by ring spectra, the product on the spectrum giving rise to the cup products in the theory.

(

**5575**views)

**E 'Infinite' Ring Spaces and E 'Infinite' Ring Spectra**

by

**J. P. May**-

**Springer**,

**1977**

The theme of this book is infinite loop space theory and its multiplicative elaboration. The main goal is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory.

(

**7775**views)

**The Homology of Iterated Loop Spaces**

by

**F. R. Cohen, T. J. Lada, P. J. May**-

**Springer**,

**2009**

A thorough treatment of homology operations and of their application to the calculation of the homologies of various spaces. The book studies an up to homotopy notion of an algebra over a monad and its role in the theory of iterated loop spaces.

(

**5866**views)

**The Geometry of Iterated Loop Spaces**

by

**J. P. May**-

**Springer**,

**1972**

A paper devoted to the study of iterated loop spaces. Our goal is to develop a simple and coherent theory which encompasses most of the known results about such spaces. We begin with some history and a description of the desiderata of such a theory.

(

**6368**views)

**A Concise Course in Algebraic Topology**

by

**J. P. May**-

**University Of Chicago Press**,

**1999**

This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics. Most chapters end with problems that further explore and refine the concepts presented.

(

**13780**views)

**Introduction to Characteritic Classes and Index Theory**

by

**Jean-Pierre Schneiders**-

**Universidade de Lisboa**,

**2000**

This text deals with characteristic classes of real and complex vector bundles and Hirzebruch-Riemann-Roch formula. We will present a few basic but fundamental facts which should help the reader to gain a good idea of the mathematics involved.

(

**5639**views)

**Elementary Topology**

by

**O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov**-

**American Mathematical Society**,

**2008**

This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space.

(

**11286**views)

**Algebraic and Geometric Topology**

by

**Andrew Ranicki, Norman Levitt, Frank Quinn**-

**Springer**,

**1985**

The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.

(

**11166**views)

**The Classification Theorem for Compact Surfaces**

by

**Jean Gallier, Dianna Xu**,

**2009**

In this book the authors present the technical tools needed for proving rigorously the classification theorem, give a detailed proof using these tools, and also discuss the history of the theorem and its various proofs.

(

**10309**views)

**Algebraic Topology**

by

**Allen Hatcher**-

**Cambridge University Press**,

**2001**

Introductory text suitable for use in a course or for self-study, it covers fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The geometric aspects of the subject are emphasized.

(

**29847**views)