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Vector Bundles and K Theory
This book contains below topics, Direct Sums, Inner Products, Tensor Product s, Associated Fiber Bundles, Clutching Functions, The Universal Bundle, Cell Structures on Grassmannians, Paracompac tness, The Fundamental Product Theorem, Deducing Periodicity from the Product T heorem, Extending to a Cohomology Theory.
Author(s): Allen Hatcher
124 Pages 
This book contains below topics, Direct Sums, Inner Products, Tensor Product s, Associated Fiber Bundles, Clutching Functions, The Universal Bundle, Cell Structures on Grassmannians, Paracompac tness, The Fundamental Product Theorem, Deducing Periodicity from the Product T heorem, Extending to a Cohomology Theory.
Author(s): Allen Hatcher
124 Pages
This paper considers smooth extensions of cohomology theories. It constructs a multiplicative model of smooth K theory, and a push forward for a proper submersion with a smooth K orientation. It also lifts the Chern character to this smooth setting.
Author(s): Ulrich Bunke, Thomas Schick
93 Pages
Algebraic K theory of real topological K theory
This book contains below topics, Hochschild homology and motivic filtrations, Filtering the motivic associated graded, Detection, Prismatic cohomology, Syntomic cohomology, Topological cyclic homology and algebraic Ktheory.
Author(s): Gabriel Angelini-Knoll, Christian Ausoni, John Rognes
59 Pages
This book contains below topics, Prerequisites, General properties of the Kgroup of a TPC, Filtered chain complexes, Barcodes step functions and Ktheory for persistence modules, A Ktheoretic pairing, Measurements on the Kgroup and on barcodes, Symplectic Applications.
Author(s): Paul Biran, Octav Cornea, Jun Zhang
68 Pages
These are lecture notes for an introductory course on Whitehead, Reidemeister, and Ray Singer torsions. This note contains below topics, Whitehead group, Torsion of a chain complex, Whitehead torsion for CW complexes, Reidemeister torsion, Lens spaces, Some applications and properties of torsions, Analytic torsion.
Author(s): Pavel Mnev
62 Pages
Lecture Notes for Algebraic and Hermitian K Theory
This note covers the following topics, Recollections and preliminaries, Symmetric monoidal and stable categories, The group completion theorem and the K theory of finite fields, The K theory of stable categories.
Author(s): Fabian Hebestreit, University of Bonn
257 Pages
Lectures on Algebraic K theory by JF Jardine
This note covers the following topics, Some homotopy theory, Exact categories, Qconstruction, Fundamental groupoid, Waldhausens constructions, Additivity, The Ktheory spectrum, Products, Group completion, Q theorem, The defining acyclic map, Homotopy fibres, Resolution theorem, Dévissage, Abelian category localization, Coherent sheaves and open subschemes, Product formulas, Ktheory with finite coefficients, Homology, Ktheory of graded rings, Homotopy property, Rigidity, Ktheory of finite fields.
Author(s): J.F. Jardine
NA Pages
This note introduces the definitions of the Ktheory groups such as The group K0, The group K1, The group K2 and Higher Ktheory groups.
Author(s): Olivier Isely
45 Pages