20/05/15 23:04:47.21 Jy/2KfWb.net
>>744
どうも
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立派な修論ですね～（＾＾；
URLﾘﾝｸ(arxiv.org)
[Submitted on 11 Feb 2019 (v1), last revised 24 Aug 2019 (this version, v3)]
A topological approach to indices of geometric operators on manifolds with fibered boundaries
Mayuko Yamashita
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 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.
Comments: 69 pages; the final version
Subjects: K-Theory and Homology (math.KT); Differential Geometry (math.DG)