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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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Polynomials and the Steenrod Algebra
by Grant Walker, Reg Wood - University of Manchester , 2010
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.