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arXiv · 2410.14188

The cyclic bar construction and fundamental groups

Nir Gadish
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Abstract

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.

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Nir Gadish. 2024-10-18. The cyclic bar construction and fundamental groups. https://arxiv.org/abs/2410.14188

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