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15 May 2017 Involutive Heegaard Floer homology
Kristen Hendricks, Ciprian Manolescu
Duke Math. J. 166(7): 1211-1299 (15 May 2017). DOI: 10.1215/00127094-3793141

Abstract

Using the conjugation symmetry on Heegaard Floer complexes, we define a 3-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to Z4-equivariant Seiberg–Witten Floer homology. Further, we obtain two new invariants of homology cobordism, d̲ and d¯, and two invariants of smooth knot concordance, V̲0 and V¯0. We also develop a formula for the involutive Heegaard Floer homology of large integral surgeries on knots. We give explicit calculations in the case of L-space knots and thin knots. In particular, we show that V̲0 detects the nonsliceness of the figure-eight knot. Other applications include constraints on which large surgeries on alternating knots can be homology-cobordant to other large surgeries on alternating knots.

Citation

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Kristen Hendricks. Ciprian Manolescu. "Involutive Heegaard Floer homology." Duke Math. J. 166 (7) 1211 - 1299, 15 May 2017. https://doi.org/10.1215/00127094-3793141

Information

Received: 24 November 2015; Revised: 12 July 2016; Published: 15 May 2017
First available in Project Euclid: 11 January 2017

zbMATH: 1383.57036
MathSciNet: MR3649355
Digital Object Identifier: 10.1215/00127094-3793141

Subjects:
Primary: 57R58
Secondary: 57M27

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 7 • 15 May 2017
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