5 papers
A survey on mapping class groups of 3-manifolds
Philipp Bader, Rachael Boyd, Giulia Carfora +8
We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold . We provide a guide to the literature and sketch proofs for var…
Smooth stable isotopy of topologically isotopic surfaces
Daniel Galvin, Patrick Orson, Mark Powell
A stabilisation of a -manifold is the connected sum of with some number of copies of . If two smooth surfaces in a -manifold are topologically isotopic…
Some remarks on -cobordisms between smooth 4-manifolds
Alexander Kupers, Mark Powell
It is not known whether the realisation part of the -cobordism theorem holds for smooth 4-manifolds, nor whether every pair of smoothly -cobordant 4-manifolds is also smoothl…
Generalised doubles and simple homotopy types of high dimensional manifolds
Csaba Nagy, John Nicholson, Mark Powell
We characterise the set of fundamental groups for which there exist -manifolds that are -cobordant (hence homotopy equivalent) but not simple homotopy equivalent, when is…
Simple homotopy types of even dimensional manifolds
Csaba Nagy, John Nicholson, Mark Powell
Given a closed -manifold, we consider the set of simple homotopy types of -manifolds within its homotopy type, called its simple homotopy manifold set. We characterise it in…