Self-adjoint local boundary problems on compact surfaces. I. Spectral flow

Prokhorova, Marina

doi:10.1007/s12220-019-00313-0

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Self-adjoint local boundary problems on compact surfaces. I. Spectral flow

MPS-Authors

/persons/resource/persons236028

Prokhorova, Marina
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s12220-019-00313-0
(Publisher version)

https://doi.org/10.48550/arXiv.1703.06105
(Preprint)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Prokhorova, M. (2021). Self-adjoint local boundary problems on compact surfaces. I. Spectral flow. The Journal of Geometric Analysis, 31(2), 1510-1554. doi:10.1007/s12220-019-00313-0.

Cite as: https://hdl.handle.net/21.11116/0000-0007-8D2A-C

Abstract

The paper deals with first order self-adjoint elliptic differential operators
on a smooth compact oriented surface with non-empty boundary. We consider such
operators with self-adjoint local boundary conditions. The paper is focused on
paths in the space of such operators connecting two operators conjugated by a
unitary automorphism. The first result is the computation of the spectral flow
for such paths in terms of the topological data over the boundary. The second
result is the universality of the spectral flow: we show that the spectral flow
is a universal additive invariant for such paths, if the vanishing on paths of
invertible operators is required.
In the next paper of the series we generalize these results to families of
such operators parametrized by points of an arbitrary compact space instead of
an interval. The integer-valued spectral flow is replaced then by the family
index taking values in the $K^1$-group of the base space.