2019/02/28 by Mayuko Yamashita
Mathematics · #Advanced Operator Algebra Research #Boundary (topology) #Deformation (meteorology) #Fibered knot #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Operator (biology) #Pairing #Signature (topology) #Topological index #Topology (electrical circuits) #math.DG #math.KT
paper · pdf · doi:10.1007/s00220-019-03595-1
69 pages; the final version
openalex created_date 2019/03/11 · arxiv created 2019/08/24 · openalex publication_date 2019/11/03 · arxiv updated 2020/01/08 · openalex updated_date 2026/08/05
Abstract In this paper, we investigate topological aspects of indices of twisted geometric operators on manifolds equipped with fibered boundaries. We define K -groups relative to the pushforward for boundary fibration, and show that indices of twisted geometric operators, defined by complete Φ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Φ</mml:mi></mml:math> or edge metrics, can be regarded as the index pairing over these K -groups. We also prove various properties of these indices using groupoid deformation techniques. Using these properties, we give an application to the localization problem of signature operators for singular fiber bundles.