An infinite-rank summand of the homology cobordism group

Abstract

We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains a ${\mathbb{Z}}^{\infty }$-subgroup and a $\mathbb{Z}$-summand. Our proof proceeds by introducing an algebraic variant of the involutive Heegaard Floer package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is inspired by an analogous argument in the setting of knot concordance due to the second author.

arXiv comment50 pages, 14 figures; added some minor lemmas

References in corpus (6)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• The knot Floer complex and the smooth concordance group
• The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
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Cited by in corpus (4)

• Linear independence of rationally slice knots
• Ozsvath-Szabo $d$-invariants of almost simple linear graphs
• Homology concordance and knot Floer homology
• Patterns in the Lattice Homology of Seifert Homology Spheres