An infinite-rank summand of the homology cobordism group

Irving Dai; Jennifer Hom; Matthew Stoffregen; Linh Truong

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arXiv · 1810.06145

An infinite-rank summand of the homology cobordism group

Irving Dai·Jennifer Hom·Matthew Stoffregen·Linh Truong

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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.

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Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong. 2018-10-15. An infinite-rank summand of the homology cobordism group. https://arxiv.org/abs/1810.06145

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