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Your search keyword '"19J25, 19K99"' showing total 2 results
Start Over Descriptor "19J25, 19K99" Topic k-theory and homology (math.kt)
2 results on '"19J25, 19K99"'

1. On the relative $L$-theory and the relative signature of PL manifolds with boundary

Author

Hou, Bingzhe and Liu, Hongzhi

Subjects
19J25, 19K99, Mathematics - K-Theory and Homology, FOS: Mathematics, Algebraic Topology (math.AT), K-Theory and Homology (math.KT), Mathematics - Algebraic Topology
Abstract

In this paper, we give a new description of the group structure of the relative structure group of PL manifolds with boundary, and obtain a surgery exact sequence in the category of groups. Then we focus on the relative $L$-group of PL manifolds with boundary, and map it to the $K$-theory additively., Comment: 31 pages, 2 figures

Published
2019
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2. The surgery exact sequence, K-theory and the signature operator

Author

Paolo Piazza and Thomas Schick

Subjects
Mathematics - Differential Geometry, 0209 industrial biotechnology, 46L87, Boundary (topology), 02 engineering and technology, signature operator, K-theory, exact surgery sequence, index classes, rho-classes, Assessment and Diagnosis, 01 natural sciences, Mathematics - Geometric Topology, 020901 industrial engineering & automation, FOS: Mathematics, Direct proof, 0101 mathematics, Topology (chemistry), Mathematics, Sequence, 19J25, 19K99, 010102 general mathematics, K-Theory and Homology (math.KT), Geometric Topology (math.GT), 58J22, Algebra, Transformation (function), Signature operator, Differential Geometry (math.DG), Surgery exact sequence, Mathematics - K-Theory and Homology, Geometry and Topology, 46L80, Analysis
Abstract

The main result of this paper is a new and direct proof of the natural transformation from the surgery exact sequence in topology to the analytic K-theory sequence of Higson and Roe. Our approach makes crucial use of analytic properties and new index theorems for the signature operator on Galois coverings with boundary. These are of independent interest and form the second main theme of the paper. The main technical novelty is the use of large scale index theory for Dirac type operators that are perturbed by lower order operators., Comment: 29 pages, AMS-LaTeX; v2: small corrections and (hopefully) improved exposition, as suggested by the referee. Final version, to appear in Annals of K-Theory

Published
2013
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