Chirality in topology and combinatorics

A Möbius strip is chiral: It has a right-handed and a left-handed version, where one cannot be deformed into the other. Any space that embeds into $R^d$ is not chiral in $R^{d+1}$. I will explain that general non-embeddabilty results may be extended to chirality results. In fact, one can use the combinatorics of triangulations of a space $X$ to lower bound the topology of the space of embeddings of $X$ into Euclidean space. This chirality phenomenon can also be explored in combinatorics. Here chirality translates into chromatic mixing for graphs, and this viewpoint gives a generalization of Lovász's general topological lower bound for the chromatic number to additionally prohibit chromatic mixing.

The topological part is joint with Michael Harrison, the combinatorial part is joint with Gunmay Handa.