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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{friedman2026cohomology,
  title = {{Bar cohomology of links: beyond Milnor invariants}},
  author = {Greg Friedman and Nir Gadish and Robin Koytcheff and Dev Sinha and Ben Walter},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.11009},
  eprint = {2609.11009},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11009},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bar cohomology of links: beyond Milnor invariants
AU  - Greg Friedman
AU  - Nir Gadish
AU  - Robin Koytcheff
AU  - Dev Sinha
AU  - Ben Walter
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.11009
UR  - https://arxiv.org/abs/2609.11009
AB  - 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.
ER  -