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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| Vydáno v: | Compositio mathematica Ročník 154; číslo 12; s. 2681 - 2700 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
London
Cambridge University Press
01.12.2018
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| Témata: | |
| ISSN: | 0010-437X, 1570-5846 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0010-437X 1570-5846 |
| DOI: | 10.1112/S0010437X18007510 |