6 papers
Simple Slice Surfaces
Mark Pencovitch
Given a simply-connected -manifold with boundary the -sphere, we give sufficient conditions for a knot in the boundary to bound a simply embedded locally flat surface in the…
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…
On the detection of knots by their traces in high dimensions
Valentina Bais, Alessio Di Prisa, Daniel Hartman +8
For every , we demonstrate the existence of non-isotopic, smooth -knots in with diffeomorphic traces. We give two proofs: the first by generalising the RBG l…
Simply slicing knots
Anthony Conway, Patrick Orson, Mark Pencovitch
Given a simply-connected 4-manifold with boundary the 3-sphere, this paper establishes sufficient conditions for a knot in the boundary to be sliced by a locally flat disc in the 4…
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…
Unknotting Nonorientable Surfaces of Genus 4 and 5
Mark Pencovitch
Expanding on work by Conway, Orson, and Powell, we study the isotopy classes rel. boundary of nonorientable, compact, locally flatly embedded surfaces in with knot group $\ma…