# Self-homeomorphisms of product of the sphere by the circle [duplicate]

What is the classification of the self-homeomorphisms of the product of the $n$-sphere by the circle, $S^n\times S^1$, when $n>3$, up to pseudo-isotopy (that is, concordance)?
• I do not understand the 1st question: Are you asking for the description of the group of self-homeomorphisms of the triangulated surface? Then it is a finite split extension of the direct product of finitely many copies of $Homeo(S^1;T)$ where $T\subset S^1$ is a 3-element subset. (The types of finite extensions are given by finite subgroups of $O(3)$.) I do not think one can get much beyond this description. – Misha Feb 11 '17 at 4:28