arXiv subjects

Mayuko Yamashita

Publications and source records attributed to Mayuko Yamashita.

20 records · Page 2Linked to original sources

arXiv2020

A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification

The Atiyah-Patodi-Singer index theorem describes the bulk-edge correspondence of symmetry protected topological insulators. The mathematical setup for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a non-local and unnatural boundary condition known as the "APS boundary condition" by hand. In 2017, we showed that the same integer as the APS index can be obtained from the $η$ invariant of the domain-wall Dirac operator. Recently we gave a mathematical proof that the equivalence is not a coincidence but generally true. In this contribution to the proceedings of LATTICE 2019, we try to explain the whole story in a physicist-friendly way.

hep-lat↗

arXiv2019

A topological approach to indices of geometric operators on manifolds with fibered boundaries

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.

math.KT↗