Simple balanced three-manifolds, Heegaard Floer homology and the Andrews-Curtis conjecture
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866915077371723776 |
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| author | Bagherifard, Neda Eftekhary, Eaman |
| author_facet | Bagherifard, Neda Eftekhary, Eaman |
| contents | The first author introduced a notion of equivalence on a family of $3$-manifolds with boundary, called (simple) balanced $3$-manifolds in an earlier paper and discussed the analogy between the Andrews-Curtis equivalence for group presentations and the aforementioned notion of equivalence. Motivated by the Andrews-Curtis conjecture, we use tools from Heegaard Floer theory to prove that there are simple balanced $3$-manifolds which are not in the trivial equivalence class (i.e. the equivalence class of $S^2\times [-1,1]$). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_14706 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Simple balanced three-manifolds, Heegaard Floer homology and the Andrews-Curtis conjecture Bagherifard, Neda Eftekhary, Eaman Geometric Topology 57M27, 57R58 The first author introduced a notion of equivalence on a family of $3$-manifolds with boundary, called (simple) balanced $3$-manifolds in an earlier paper and discussed the analogy between the Andrews-Curtis equivalence for group presentations and the aforementioned notion of equivalence. Motivated by the Andrews-Curtis conjecture, we use tools from Heegaard Floer theory to prove that there are simple balanced $3$-manifolds which are not in the trivial equivalence class (i.e. the equivalence class of $S^2\times [-1,1]$). |
| title | Simple balanced three-manifolds, Heegaard Floer homology and the Andrews-Curtis conjecture |
| topic | Geometric Topology 57M27, 57R58 |
| url | https://arxiv.org/abs/2205.14706 |