Algebraic Topology Class Notes (PDF 119P)

Algebraic Topology Lecture Notes by Christian Bar

This note expplains the following topics: set theoretic topology, Homotopy theory and homology theory.

Author(s): Christian Bar

172 Pages

Lectures on Algebraic Topology by Haynes Miller

This PDF Lectures covers the following topics related to Algebraic Topology : Singular homology, Introduction: singular simplices and chains, Homology, Categories, functors, and natural transformations, Basic homotopy theory, The homotopy theory of CW complexes, Vector bundles and principal bundles, Spectral sequences and Serre classes, Characteristic classes, Steenrod operations, and cobordism.

Author(s): Haynes Miller

307 Pages

Algebraic Topology A Comprehensive Introduction

This book explains the following topics: Introduction, Fundamental group, Classification of compact surfaces, Covering spaces, Homology, Basics of Cohomology, Cup Product in Cohomology, Poincaré Duality, Basics of Homotopy Theory, Spectral Sequences. Applications, Fiber bundles, Classifying spaces, Applications, Vector Bundles, Characteristic classes, Cobordism, Applications.

Author(s): Laurentiu Maxim, University of Wisconsin-Madison

318 Pages

Algebraic Topology by NPTEL

This is a basic note in algebraic topology, it introduce the notion of fundamental groups, covering spaces, methods for computing fundamental groups using Seifert Van Kampen theorem and some applications such as the Brouwer’s fixed point theorem, Borsuk Ulam theorem, fundamental theorem of algebra.

Author(s): Prof. G.K. Srinivasan

NA Pages

Algebraic Topology by Andreas Kriegl

This note explains the following topics: Building blocks and homeomorphy, Homotopy, Simplicial Complexes,CW-Spaces, Fundamental Group , Coverings, Simplicial Homology and Singular Homology.

Author(s): Andreas Kriegl

125 Pages

Topics in Algebraic Topology The Sullivan Conjecture

The goal of this note is to describe some of the tools which enter into the proof of Sullivan's conjecture. Topics covered includes: Steenrod operations, The Adem relations, Admissible monomials, Free unstable modules,  A theorem of Gabriel-Kuhn-Popesco, Injectivity of the cohomology of BV, Generating analytic functors, Tensor products and algebras, Free unstable algebras, The dual Steenrod algebra, The Frobenius, Finiteness conditions, Injectivity of tensor products, Lannes T-functor, The T-functor and unstable algebras, Free E-infinity algebras, A pushout square, The Eilenberg-Moore spectral sequence, Operations on E-infinity algebras, The Sullivan conjecture.

Author(s): Prof. Jacob Lurie

NA Pages

Introduction To Algebraic Topology And Algebraic Geometry

This note provides an introduction to algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. Covered topics are: Algebraic Topology, Singular homology theory, Introduction to sheaves and their cohomology, Introduction to algebraic geometry, Complex manifolds and vector bundles, Algebraic curves.

Author(s): Genova

138 Pages

Algebraic Topology by Michael Starbird

Much of topology is aimed at exploring abstract versions of geometrical objects in our world. The concept of geometrical abstraction dates back at least to the time of Euclid. All of the objects that we will study in this note will be subsets of the Euclidean spaces. Topics covered includes: 2-manifolds, Fundamental group and covering spaces, Homology, Point-Set Topology, Group Theory, Graph Theory and The Jordan Curve Theorem.

Author(s): Michael Starbird

127 Pages