PIN(2)-monopole Floer homology and the Rokhlin invariant
We show that the bar version of the $\text{Pin}(2)$ -monopole Floer homology of a three-manifold $Y$ equipped with a self-conjugate spin $^{c}$ structure $\mathfrak{s}$ is determined by the triple cup product of $Y$ together with the Rokhlin invariants of the spin structures inducing $\mathfrak{s}$...
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| Published in: | Compositio mathematica Vol. 154; no. 12; pp. 2681 - 2700 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
London
Cambridge University Press
01.12.2018
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| Subjects: | |
| ISSN: | 0010-437X, 1570-5846 |
| Online Access: | Get full text |
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| Summary: | We show that the bar version of the
$\text{Pin}(2)$
-monopole Floer homology of a three-manifold
$Y$
equipped with a self-conjugate spin
$^{c}$
structure
$\mathfrak{s}$
is determined by the triple cup product of
$Y$
together with the Rokhlin invariants of the spin structures inducing
$\mathfrak{s}$
. This is a manifestation of mod
$2$
index theory and can be interpreted as a three-dimensional counterpart of Atiyah’s classical results regarding spin structures on Riemann surfaces. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0010-437X 1570-5846 |
| DOI: | 10.1112/S0010437X18007510 |