On entropies, $\mathcal{F}$-structures, and scalar curvature of certain involutions

Abstract

In this short note, we analyze geometric properties of orbit spaces of certain involutions in dimensions four, five, and six. We consider constructions of $\mathcal{F}$-structures on manifolds of dimension at least four that allows us to study minimal entropy, minimal volume, collapse with bounded curvature, and sign of the Yamabe invariant building on work of Paternain-Petean. The existence of Riemannian metrics of vanishing topological entropy on the orbit spaces is investigated as well.

Added result regarding the minimal entropy and value of the Yamabe invariant of the inequivalent smooth structures on elliptic surfaces that are built using Fintushel-Stern's Knot surgery

References in corpus (1)

• Round handles, logarithmic transforms, and smooth 4-manifolds