For smooth surfaces, the generic singularities of a map of one surface to another are folds and cusps (Whitney). It is a standard result in singularity theory that the generic isotopy of such a map is ...
What is known about the distribution of average edge-degrees for 3-manifold triangulations (with the number of 3-simplices less than a fixed constant)?
This is my first question on mathoverflow! It relates to a project I'm undertaking with a student. Work by Tamura (extending results by Luo and Stong) shows that for any closed 3-manifold $M$ and any ...
Let $N$ and $N'$ be regular neighborhoods of a subpolyhedron $P$ in a closed PL manifold $M$, and suppose that $t$ is a free PL involution on $M$ such that each of $\partial N$, $\partial N'$ is ...