INVOLUTIVE HEEGAARD FLOER HOMOLOGY AND PLUMBED THREE-MANIFOLDS

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...

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Bibliographic Details
Published in:Journal of the Institute of Mathematics of Jussieu 2019-11, Vol.18 (6), p.1115-1155, Article 1115
Main Authors: Dai, Irving, Manolescu, Ciprian
Format: Article
Language:English
Subjects:
Homology
Subgroups
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Summary: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.
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748017000329