An infinite-rank summand of the homology cobordism group
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866929473113292800 |
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| author | Dai, Irving Hom, Jennifer Stoffregen, Matthew Truong, Linh |
| author_facet | Dai, Irving Hom, Jennifer Stoffregen, Matthew Truong, Linh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_06145 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An infinite-rank summand of the homology cobordism group Dai, Irving Hom, Jennifer Stoffregen, Matthew Truong, Linh Geometric Topology 57M27, 57R58 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. |
| title | An infinite-rank summand of the homology cobordism group |
| topic | Geometric Topology 57M27, 57R58 |
| url | https://arxiv.org/abs/1810.06145 |