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2017 The surgery exact triangle in $\mathrm{Pin}(2)\mskip-1.5mu$–monopole Floer homology
Francesco Lin
Algebr. Geom. Topol. 17(5): 2915-2960 (2017). DOI: 10.2140/agt.2017.17.2915

Abstract

We prove the existence of an exact triangle for the Pin(2)–monopole Floer homology groups of three-manifolds related by specific Dehn surgeries on a given knot. Unlike the counterpart in usual monopole Floer homology, only two of the three maps are those induced by the corresponding elementary cobordism. We use this triangle to describe the Manolescu correction terms of the manifolds obtained by (±1)–surgery on alternating knots with Arf invariant 1.

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Francesco Lin. "The surgery exact triangle in $\mathrm{Pin}(2)\mskip-1.5mu$–monopole Floer homology." Algebr. Geom. Topol. 17 (5) 2915 - 2960, 2017. https://doi.org/10.2140/agt.2017.17.2915

Information

Received: 29 September 2016; Revised: 20 January 2017; Accepted: 7 February 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06791389
MathSciNet: MR3704248
Digital Object Identifier: 10.2140/agt.2017.17.2915

Subjects:
Primary: 57M27

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 5 • 2017
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