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Algebraic Topology

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K-theory (7)

e-books in Algebraic Topology category

Book cover: An Elementary Illustrated Introduction to Simplicial SetsAn Elementary Illustrated Introduction to Simplicial Sets
by - arXiv.org ,
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.
(2906 views)
Book cover: Topological Groups: Yesterday, Today, TomorrowTopological Groups: Yesterday, Today, Tomorrow
by - MDPI AG ,
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.
(1000 views)
Book cover: Modern Algebraic TopologyModern Algebraic Topology
by - Macmillan ,
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.
(1778 views)
Book cover: Differential Forms and Cohomology: CourseDifferential Forms and Cohomology: Course
by - Intelligent Perception ,
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.
(2350 views)

Book cover: Topology IllustratedTopology Illustrated
by - Intelligent Perception ,
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.
(1906 views)
Book cover: Lectures on Introduction to Algebraic TopologyLectures on Introduction to Algebraic Topology
by - Tata Institute of Fundamental Research ,
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.
(4373 views)
Book cover: Algebraic and Geometric SurgeryAlgebraic and Geometric Surgery
by - Oxford University Press ,
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.
(4343 views)
Book cover: Topology of Stratified SpacesTopology of Stratified Spaces
by - Cambridge University Press ,
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.
(3933 views)
Book cover: Manifold TheoryManifold Theory
by - UCLA ,
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.
(4252 views)
Book cover: Introduction to Algebraic Topology and Algebraic GeometryIntroduction to Algebraic Topology and Algebraic Geometry
by ,
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.
(5322 views)
Book cover: Higher Topos TheoryHigher Topos Theory
by - Princeton University Press ,
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.
(6074 views)
Book cover: Notes on the course Algebraic TopologyNotes on the course Algebraic Topology
by - University of Oregon ,
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.
(4585 views)
Book cover: Introduction to Topological GroupsIntroduction to Topological Groups
by - UCM ,
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.
(5021 views)
Book cover: Polynomials and the Steenrod AlgebraPolynomials and the Steenrod Algebra
by - University of Manchester ,
This book investigates the Steenrod algebra A2 over the field of two elements F2 in a purely algebraic context by its action on the polynomial algebra P(n) in n variables over F2. The reader is expected to have a basic knowledge of algebra.
(4611 views)
Book cover: Geometry of 2D Topological Field TheoriesGeometry of 2D Topological Field Theories
by - arXiv ,
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.
(6617 views)
Book cover: A Primer on Homotopy ColimitsA Primer on Homotopy Colimits
by - University of Oregon ,
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.
(4323 views)
Book cover: A Topology PrimerA Topology Primer
by - Technische Universit├Ąt Kaiserslautern ,
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.
(6685 views)
Book cover: Lecture Notes on Motivic CohomologyLecture Notes on Motivic Cohomology
by - AMS ,
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.
(4428 views)
Book cover: Topics in topology: The signature theorem and some of its applicationsTopics in topology: The signature theorem and some of its applications
by - University of Notre Dame ,
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.
(4516 views)
Book cover: Prerequisites in Algebraic TopologyPrerequisites in Algebraic Topology
by - NTNU ,
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.
(5281 views)
Book cover: Homotopy Theories and Model CategoriesHomotopy Theories and Model Categories
by - University of Notre Dame ,
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.
(4445 views)
Book cover: The Adams-Novikov Spectral Sequence and the Homotopy Groups of SpheresThe Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres
by - Northwestern University ,
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.
(6804 views)
Book cover: Topology Lecture NotesTopology Lecture Notes
by - UEA ,
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.
(6266 views)
Book cover: An Introduction to Algebraic SurgeryAn Introduction to Algebraic Surgery
by - arXiv ,
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.
(5321 views)
Book cover: sclscl
by - Mathematical Society of Japan ,
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.
(4521 views)
Book cover: Lectures on Etale CohomologyLectures on Etale Cohomology
by ,
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.
(4328 views)
Book cover: Equivariant Stable Homotopy TheoryEquivariant Stable Homotopy Theory
by - Springer ,
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.
(8672 views)
Book cover: H Ring Spectra and Their ApplicationsH Ring Spectra and Their Applications
by - Springer ,
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.
(4677 views)
Book cover: E 'Infinite' Ring Spaces and E 'Infinite' Ring SpectraE 'Infinite' Ring Spaces and E 'Infinite' Ring Spectra
by - Springer ,
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.
(6588 views)
Book cover: The Homology of Iterated Loop SpacesThe Homology of Iterated Loop Spaces
by - Springer ,
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.
(4854 views)
Book cover: The Geometry of Iterated Loop SpacesThe Geometry of Iterated Loop Spaces
by - Springer ,
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.
(5196 views)
Book cover: A Concise Course in Algebraic TopologyA Concise Course in Algebraic Topology
by - University Of Chicago Press ,
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.
(12571 views)
Book cover: Introduction to Characteritic Classes and Index TheoryIntroduction to Characteritic Classes and Index Theory
by - Universidade de Lisboa ,
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.
(4711 views)
Book cover: Elementary TopologyElementary Topology
by - American Mathematical Society ,
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.
(9921 views)
Book cover: Algebraic and Geometric TopologyAlgebraic and Geometric Topology
by - Springer ,
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.
(9855 views)
Book cover: The Classification Theorem for Compact SurfacesThe Classification Theorem for Compact Surfaces
by ,
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.
(9361 views)
Book cover: Algebraic TopologyAlgebraic Topology
by - Cambridge University Press ,
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.
(27676 views)