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INVOLUTIVE HEEGAARD FLOER HOMOLOGY AND PLUMBED THREE-MANIFOLDS

Part of: Low-dimensional topology Differential topology

Published online by Cambridge University Press:  04 September 2017

Irving Dai  and
Ciprian Manolescu Open the ORCID record for Ciprian Manolescu [Opens in a new window]
Irving Dai
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08540, USA ([email protected])
Ciprian Manolescu
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095, USA ([email protected])
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Abstract

We compute the involutive Heegaard Floer homology of the family of three-manifolds obtained by plumbings along almost-rational graphs. (This includes all Seifert fibered homology spheres.) We also study the involutive Heegaard Floer homology of connected sums of such three-manifolds, and explicitly determine the involutive correction terms in the case that all of the summands have the same orientation. Using these calculations, we give a new proof of the existence of an infinite-rank subgroup in the three-dimensional homology cobordism group.

Keywords

Floer homologyplumbings3-manifoldshomology cobordism

MSC classification

Primary: 57R58: Floer homology 57M27: Invariants of knots and 3-manifolds
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 6 , November 2019 , pp. 1115 - 1155
Copyright
© Cambridge University Press 2017 

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Footnotes

ID was partially supported by NSF grant DGE-1148900. CM was partially supported by NSF grant DMS-1402914.

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