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arXiv · 2609.11009

Bar cohomology of links: beyond Milnor invariants

Greg Friedman·Nir Gadish·Robin Koytcheff·Dev Sinha·Ben Walter
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Abstract

We develop bar cohomology of link complements as an invariant of links in homology spheres. In this setting, bar cohomology is a Hopf algebra which is calculable using surfaces and their intersection curves in a link complement. In this first in a sequence of works, we introduce the invariant and show that it defines a canonical subspace of the tensor Hopf algebra, which already encodes information about Milnor's link invariants and provides geometrically significant information beyond them.

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Greg Friedman, Nir Gadish, Robin Koytcheff, Dev Sinha, Ben Walter. 2026-09-10. Bar cohomology of links: beyond Milnor invariants. https://arxiv.org/abs/2609.11009

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