The cyclic bar construction and fundamental groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910656422215680 |
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| author | Gadish, Nir |
| author_facet | Gadish, Nir |
| contents | We determine the 0-th Hochschild homology of the associative algebra of simplicial cochains valued in a PID: it consists of the ``finite-type" homotopy invariants of free loops, equivalently finite-type class functions on the fundamental group. One major motivation for this calculation is joint work in progress aiming to geometrically construct invariants of links in the 3-sphere as well as other $3$-manifolds, and to realize Milnor's linking numbers as evaluations of 0-th Hochschild homology classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The cyclic bar construction and fundamental groups Gadish, Nir Algebraic Topology Rings and Algebras 57M05, 57K16, 20J05, 16S34, 20-08 We determine the 0-th Hochschild homology of the associative algebra of simplicial cochains valued in a PID: it consists of the ``finite-type" homotopy invariants of free loops, equivalently finite-type class functions on the fundamental group. One major motivation for this calculation is joint work in progress aiming to geometrically construct invariants of links in the 3-sphere as well as other $3$-manifolds, and to realize Milnor's linking numbers as evaluations of 0-th Hochschild homology classes. |
| title | The cyclic bar construction and fundamental groups |
| topic | Algebraic Topology Rings and Algebras 57M05, 57K16, 20J05, 16S34, 20-08 |
| url | https://arxiv.org/abs/2410.14188 |