Lecture notes on torsions

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

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

On the integral algebraic K theory of Morava K theory

This note contains below topics, On the TC of formal DGAs with polynomial homology, The May filtration on topological negative cyclic homology and topological periodic cyclic homology, Cardinality of topological cyclic homology, Coefficients in algebraically closed fields, On the algebraic Ktheory of truncated witt vectors, On the algebraic Ktheory of motivic pullback squares, Bockstein spectral sequences and syntomic cohomology, On the K 1 local algebraic Ktheory of K 1.

Author(s): Gabriel Angelini-Knoll, Haldun Özgür Bay?nd?r

58 Pages

Lecture notes on torsions

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

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