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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 
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
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
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
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