On the involutive Heegaard Floer homology of negative semidefinite plumbed 3-manifolds with b1 = 1

Johnson, Peter K¹

¹Department of Mathematics, University of Virginia, Charlottesville, VA, United States

Algebraic and Geometric Topology, Tome 25 (2025) no. 2, pp. 827-885

Résumé

Ozsváth and Szabó (2003) used Heegaard Floer homology to define numerical invariants d1∕2 and d−1∕2 for 3-manifolds Y with H1(Y ; ℤ)≅ ⁡ℤ. We define involutive Heegaard Floer theoretic versions of these invariants analogous to the involutive d invariants d¯ and d¯ defined for rational homology spheres by Hendricks and Manolescu (2017). We prove their invariance under spin integer homology cobordism and use them to establish spin filling constraints and 0-surgery obstructions analogous to results by Ozsváth and Szabó for their Heegaard Floer counterparts d1∕2 and d−1∕2. We then apply calculation techniques of Dai and Manolescu (2019) and Rustamov (2004) to compute the involutive Heegaard Floer homology of some negative semidefinite plumbed 3-manifolds with b1 = 1. By combining these calculations with the 0-surgery obstructions, we are able to produce an infinite family of small Seifert fibered spaces with weight 1 fundamental group and first homology ℤ which cannot be obtained by 0-surgery on a knot in S3, extending a result of Hedden, Kim, Mark and Park (2019).

Détail

DOI : 10.2140/agt.2025.25.827

Keywords: involutive Heegaard Floer homology, plumbed manifolds, negative semidefinite, 0-surgery, Seifert fibered space

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