Abstract:
We say that a $d$-dimensional simplicial complex embeds into double dimension
if it embeds into the Euclidean space of dimension $2d$. For instance, a
graph is planar iff it embeds into double dimension. If two simplicial
complexes $K$ and $L$ are not embeddable into double dimension, what can we say
about their join complex $K*L$? In this talk, I consider this problem and
show that quite unexpectedly there are complexes $K$ and $L$ which are not
embeddable into double dimension, but their join is embeddable into double
dimension. More generally, I discuss conditions under which the join is
non-embeddable into double dimension. The integer Smith classes are our
main tool and I discuss these classes and how they behave under the join of
complexes with actions of prime period.
