Spaces of embeddings: Nonsingular bilinear maps, chirality, and their generalizations

Frick, Florian; Harrison, Michael

doi:10.1090/proc/15752

Spaces of embeddings: Nonsingular bilinear maps, chirality, and their generalizations
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by Florian Frick and Michael Harrison PDF

Proc. Amer. Math. Soc. 150 (2022), 423-437 Request permission

Abstract:

Given a space $X$ we study the topology of the space of embeddings of $X$ into $\mathbb {R}^d$ through the combinatorics of triangulations of $X$. We give a simple combinatorial formula for upper bounds for the largest dimension of a sphere that antipodally maps into the space of embeddings. This result summarizes and extends results about the nonembeddability of complexes into $\mathbb {R}^d$, the nonexistence of nonsingular bilinear maps, and the study of embeddings into $\mathbb {R}^d$ up to isotopy, such as the chirality of spatial graphs.

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