P. Orson

activity

20242026

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6 papers · 1 filter

math.GT2026

Stably exotic fillings of 3-manifolds

Daniel Kasprowski, Patrick Orson, Mark Powell +1

We investigate which 3-manifolds bound 4-manifolds that are homeomorphic but not stably diffeomorphic, where stabilising means taking connected sum with copies of $S^{2} \times S^{2}$ .…

math.GT2026

Smooth stable isotopy of topologically isotopic surfaces

Daniel Galvin, Patrick Orson, Mark Powell

A stabilisation of a $4$ -manifold $X$ is the connected sum of $X$ with some number of copies of $S^{2} \times S^{2}$ . If two smooth surfaces in a $4$ -manifold are topologically isotopic…

math.GT2025

Smoothing topological pseudo-isotopies of 4-manifolds

Patrick Orson, Mark Powell, Oscar Randal-Williams

Given a closed, smooth 4-manifold $X$ and self-diffeomorphism $f$ that is topologically pseudo-isotopic to the identity, we study the question of whether $f$ is moreover smoothly p…

math.GT2025

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…

math.GT2024

Unknotting nonorientable surfaces

Anthony Conway, Patrick Orson, Mark Powell

Given a nonorientable, locally flatly embedded surface in the $4$ -sphere of nonorientable genus $h$ , Massey showed that the normal Euler number lies in $\lbrace -2h,-2h+4,\ldots,2h…

math.GT2024

Locally flat simple spheres in $C P^{2}$

Anthony Conway, Patrick Orson

The fundamental group of the complement of a locally flat surface in a $4$ -manifold is called the knot group of the surface. In this article we prove that two locally flat $2$ -sphe…