Automorphisms, cohomology and extensions of symmetric quandles
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912650085007360 |
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| author | Karmakar, Biswadeep Saraf, Deepanshi Singh, Mahender |
| author_facet | Karmakar, Biswadeep Saraf, Deepanshi Singh, Mahender |
| contents | It is well-known that the cohomology of symmetric quandles generates robust cocycle invariants for unoriented classical and surface links. Expanding on the recently introduced module-theoretic generalized cohomology for symmetric quandles, we derive a four-term exact sequence that relates 1-cocycles, second cohomology, and a specific group of automorphisms associated with the extensions of symmetric quandles. This exact sequence shows that the obstruction to lifting and extending automorphisms is found in the second symmetric quandle cohomology. Additionally, some general aspects of dynamical cocycles and extensions are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphisms, cohomology and extensions of symmetric quandles Karmakar, Biswadeep Saraf, Deepanshi Singh, Mahender Quantum Algebra Geometric Topology Primary 57K10, 57K12, Secondary 57K45 It is well-known that the cohomology of symmetric quandles generates robust cocycle invariants for unoriented classical and surface links. Expanding on the recently introduced module-theoretic generalized cohomology for symmetric quandles, we derive a four-term exact sequence that relates 1-cocycles, second cohomology, and a specific group of automorphisms associated with the extensions of symmetric quandles. This exact sequence shows that the obstruction to lifting and extending automorphisms is found in the second symmetric quandle cohomology. Additionally, some general aspects of dynamical cocycles and extensions are discussed. |
| title | Automorphisms, cohomology and extensions of symmetric quandles |
| topic | Quantum Algebra Geometric Topology Primary 57K10, 57K12, Secondary 57K45 |
| url | https://arxiv.org/abs/2407.02971 |