6 papers
Stably exotic knotted surfaces up to equivalence
Daniel Galvin, Daniel Kasprowski
In this short note we show the existence of stably exotic knotted surfaces in 4-manifolds in the sense that the embedded surfaces are topologically equivalent but are not smoothly…
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…
Non-smoothable surfaces in the 4-sphere
Anthony Conway, Daniel Galvin
We construct examples of non-smoothable surfaces in the -sphere, thereby answering Question 4.32 on the K3 problem list. These surfaces are non-orientable and have knot group of…
Geometric obstructions for -fillings of 3-manifolds
Daniel Galvin, Peter Teichner, Simona Veselá
We consider the realisation problem for normal 1-types of 4-manifolds with a given boundary. More precisely, given a normal 1-type and closed 3-dimensional -manifold , do…
Algorithms in 4-manifold topology
Stefan Bastl, Rhuaidi Burke, Rima Chatterjee +28
We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In p…