High dimensional knot theory

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

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

Persistence K theory

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

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

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