Algebraic K theory of real topological K theory

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

Smooth K Theory

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

Lecture Notes On The K theory Of Operator Algebras

This lecture note covers the following topics,Projections and Unitaries, The K0Group for Unital C Algebras, K1Functor and the Index Map, Bott Periodicity and the Exact Sequence of KTheory, Tools for the computation of Kgroups.

Author(s): Rainer Matthes and Wojciech Szymansk

92 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

Introduction To K theory and Some Applications

This book explains the following topics, Topological Ktheory, Ktheory of C algebras, Geometric and Topological Invarients, THE FUNCTORS K1 K2, K1, SK1 of Orders and Grouprings, Higher Algebraic Ktheory, Higher Dimensional Class Groups of Orders and Group rings, Higher Ktheory of Schemes, Modm Higher Ktheory of exact Categories, Schemes and Orders, Profinite Higher Ktheory of Exact Categories, Schemes and Orders, Equivariant Higher Ktheory Together with Relative Generalizations, Interpretation in Terms of Grouprings.

Author(s): Aderemi Kuku, University of Iowa

141 Pages

K Theory and Geometric Topology

The primary purpose of this note is to examine many of these Ktheoretic invariants, not from a historical point of view, but rather a posteriori, now that Ktheory is a mature subject.

Author(s): Jonathan Rosenberg

37 Pages

Algebraic K Theory

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