On the universal pairing for 2-complexes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911292813475840 |
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| author | Khovanov, Mikhail Krushkal, Vyacheslav Nicholson, John |
| author_facet | Khovanov, Mikhail Krushkal, Vyacheslav Nicholson, John |
| contents | The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 by Freedman et al. We prove an analogous result for 2-complexes, and also show that the universal pairing does not detect the difference between simple homotopy equivalence and 3-deformations. The question of whether these two equivalence relations are different for 2-complexes is the subject of the Andrews-Curtis conjecture. We also discuss the universal pairing for higher-dimensional complexes and show that it is not positive. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_07429 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the universal pairing for 2-complexes Khovanov, Mikhail Krushkal, Vyacheslav Nicholson, John Geometric Topology Quantum Algebra Primary: 57K16, 57K20, 20F05 The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 by Freedman et al. We prove an analogous result for 2-complexes, and also show that the universal pairing does not detect the difference between simple homotopy equivalence and 3-deformations. The question of whether these two equivalence relations are different for 2-complexes is the subject of the Andrews-Curtis conjecture. We also discuss the universal pairing for higher-dimensional complexes and show that it is not positive. |
| title | On the universal pairing for 2-complexes |
| topic | Geometric Topology Quantum Algebra Primary: 57K16, 57K20, 20F05 |
| url | https://arxiv.org/abs/2312.07429 |