Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
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 
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 of C algebras
This note contains below topics, Gelfand category and Gelfand functor, Gelfand space and Ktheory, Algebraic topology of the noncommutative torus, Hausdorff blowingup, Groupoids foliations and their coverings, Gelfand spaces of continuous trace C algebras, Appendices, Category theory, Topology, Lattices and filters, Sheaves and cohomology, C algebras, Continuous trace C algebras, C algebras of groupoids, Noncommutative torus Tn.
Author(s): Petr Ivankov
119 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
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
Algebraic Topology by Cornell University
This note covers the following topics, moduli space of flat symplectic surface bundles, Cohomology of the Classifying Spaces of Projective Unitary Groups, covering type of a space, A Maytype spectral sequence for higher topological Hochschild homology, topological Hochschild homology of the K 1 local sphere, QuasiElliptic Cohomology and its Power Operations, Local and global coincidence homology classes, Tangent categories of algebras over operads, Automorphisms of the little disks operad with ptorsion coefficients.
Author(s): Cornell University
NA Pages