Branched covers and rational homology balls
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911813573017600 |
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| author | Livingston, Charles |
| author_facet | Livingston, Charles |
| contents | The concordance group of knots in the three-sphere contains an infinite subgroup generated by elements of order two, each one of which is represented by a knot K with the property that for every n > 0, the n-fold cyclic cover of S^3 branched over K bounds a rational homology ball. This implies that the kernel of the canonical homomorphism from the knot concordance group to the infinite direct sum of rational homology cobordism groups (defined via prime-power branched covers) contains an infinitely generated two-torsion subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_06713 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Branched covers and rational homology balls Livingston, Charles Geometric Topology 57K10 The concordance group of knots in the three-sphere contains an infinite subgroup generated by elements of order two, each one of which is represented by a knot K with the property that for every n > 0, the n-fold cyclic cover of S^3 branched over K bounds a rational homology ball. This implies that the kernel of the canonical homomorphism from the knot concordance group to the infinite direct sum of rational homology cobordism groups (defined via prime-power branched covers) contains an infinitely generated two-torsion subgroup. |
| title | Branched covers and rational homology balls |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2202.06713 |