Algebraic Topology for Data Scientists

Algebraic Topology

This book contains below topics, Cell Complexes, Operations on Spaces, Two Criteria for Homotopy Equivalen ce, The Homotopy Extension Property, The van Kampen Theorem, Applications to Cell Complexes, The Classication of Covering Space s, Deck Transformations and Group Actions, Simplicial Homology, Singular Homology.

Author(s): Allen Hatcher

560 Pages

Configuration spaces in algebraic topology

This book contains below topics, Configuration spaces and braids, Cohomology of ConfkRn, Covering theorems, Deferred proofs, Mapping space models, Homology calculations from stable splittings, Mod p cohomology, Postscript Lie algebra methods, Split simplicial spaces, Homotopy colimits, The Spanier Whitehead category, Tate cohomology and periodicity.

Author(s): Ben Knudsen

117 Pages

Algebraic Topology for Data Scientists

This book contains below topics, Point Set Topology Background, Abstract Algebra Background, Traditional Homology Theory, Persistent Homology, Related Techniques, Some Unfinished Ideas, Cohomology, Homotopy Theory, Obstruction Theory, Steenrod Squares and Reduced Powers, Homotopy Groups of Spheres.

Author(s): Michael S. Postol

324 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 I Iv5 Stefan Friedl

The contents of this book include, Topological spaces, General topology, some delicate bits, Topological manifolds and manifolds, Categories, functors and natural transformations, Covering spaces and manifolds, Homotopy equivalent topological spaces, Differential topology, Basics of group theory, The basic Seifertvan Kampen Theorem, Presentations of groups and amalgamated products, The general Seifertvan Kampen Theorem, Cones, suspensions, cylinders, Limits, etc.

Author(s): Stefan Friedl

2076 Pages

Notes On The Course Algebraic Topology

This note covers the following topics, 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, Homotopy groups of CW complexes, Homology groups, Homology groups of CW complexes, Homology with coefficients and cohomology groups, Cap product and the Poincare duality, Elementary obstruction theory.

Author(s): Boris Botvinnik

181 Pages

Algebraic Topology by Andreas Kriegl

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

Author(s): Andreas Kriegl

125 Pages