SPACES OF EMBEDDINGS: NONSINGULAR BILINEAR MAPS, CHIRALITY, AND THEIR GENERALIZATIONS

Given a space X we study the topology of the space of embeddings of X into 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 R-d , the nonexistence of nonsingular bilinear maps, and the study of embeddings into R-d up to isotopy, such as the chirality of spatial graphs.