Spaces of embeddings: Nonsingular bilinear maps, chirality, and their generalizations
Florian Frick, Michael Harrison · Proceedings of the American Mathematical Society · 2021
Given a space X X we study the topology of the space of embeddings of X X into R d \mathbb {R}^d through the combinatorics of triangulations of X 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 R d \mathbb {R}^d , the nonexistence of nonsingular bilinear maps, and the study of embeddings into R d \mathbb {R}^d up to isotopy, such as the chirality of spatial graphs.