Let K be the K3 manifold. In this note, we discuss two methods to prove that certain
generalized Miller–Morita–Mumford classes for smooth bundles with fiber K are nonzero. As …

In this paper, for a group Ĝ and its normal subgroup G, we study Ĝ-invariant
quasimorphisms on G which appear in symplectic geometry and low dimensional topology …

A trisection of a smooth 4-manifold is a decomposition into three simple pieces with nice
intersection properties. Work by Gay and Kirby shows that every smooth, connected …

We give general classification and structure theorems for actions of groups of
homeomorphisms and diffeomorphisms on manifolds, reminiscent of classical results for …

We give general classification and structure theorems for actions of groups of
homeomorphisms and diffeomorphisms on manifolds, reminiscent of classical results for …

We give a short and elementary proof of the nonrealizability of the mapping class group via
homeomorphisms. This was originally established by Markovic, resolving a conjecture of …

We show that the projection Homeo+(D n 2)→ B n does not have a section for n≥ 6; ie the
braid group B n cannot be geometrically realized as a group of homeomorphisms of a disk …

Let $ M $ be an oriented smooth manifold, and $\operatorname {Homeo}(M,\omega) $ the
group of measure preserving homeomorphisms of $ M $, where $\omega $ is a finite …

Let $ N $ be a smooth manifold that is homeomorphic but not diffeomorphic to a closed
hyperbolic manifold $ M $. In this paper, we study the extent to which $ N $ admits as much …

Nielsen realization problem for the mapping class group Mod (S g) asks whether the natural
projection pg: Homeo+(S g)→ Mod (S g) has a section. While all the previous results use …