Let M be an orientable 3-dimensional small cover, i.e. a real analog of quasi-toric space with an action (Z_2)^3. Let G be a subgroup of orientation-preserving homeomorphisms in (Z_2)^3. In this talk we will discuss an orbit space of M/g for g in G. We will show that M/g is homeomorphic to S^3 or connected sum of several copies of S^1 x S^2. In the case when the orbit space is S^3 we will describe M as the double-branched covering of S^3 over a link and relate it to Hamilton cycles in polytopes. We also will discuss how this result is related to rigidity problems in toric topology.

In this talk I will define Liouville vector fields, Weinstein domains, contact type submanifolds and discuss their connection with Stein structures and rational convexity in $\mathbb C^n$.

An H-space is a topological space with a unital binary operation. The theory of H-spaces goes back to the 1950's and is closely connected to the theory of loop spaces. In this talk, I'll give some background about H-spaces and then present several new results in this area, including a property that allows us to deloop certain "central" H-spaces. While this work was done in the framework of homotopy type theory, and therefore applies in any $\infty$-topos, I will explain it in the special case of topological spaces.

This is based on joint work with Ulrik Buchholtz, Jarl Flaten, and Egbert Rijke in arxiv:2301.02636.

TBA