Mapping spaces of Swiss cheese operads

Victor Turchin

Mapping spaces of Swiss cheese operads

Algebraic Topology 2026-02-17 v3

Authors: Victor Turchin

Abstract

We show that the color restriction map $\mathrm{Op}^h({\mathcal{SC}}_m,{\mathcal{SC}}_n)\to \mathrm{Op}^h({\mathcal E}_{m-1},{\mathcal E}_{n-1})$ from the derived mapping space of Swiss cheese operads to that of little discs operads, is a weak homotopy equivalence. We explain how this can help in the study of disc concordance embedding spaces.

Keywords

Swiss cheese operads mapping spaces weak homotopy equivalence derived mapping space little discs operads

Cite

@article{arxiv.2410.02190,
  title  = {Mapping spaces of Swiss cheese operads},
  author = {Victor Turchin},
  journal= {arXiv preprint arXiv:2410.02190},
  year   = {2026}
}

Comments

10 pages. Lemma 2.1 in the previous version had a mistake found by a referee. The new version has a slightly different last step of the proof of Theorem A

Mapping spaces of Swiss cheese operads

Abstract

Keywords

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