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Lectures on Topics in Algebraic K Theory (PDF 138P)
This note covers the following topics: The exact sequence of algebraic K-theory, Categories of modules and their equivalences, Brauer group of a commutative ring, Brauer-Wall group of graded Azumaya algebras and The structure of the Clifford Functor.
Author(s): Hyman Bass
138 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
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
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
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
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