Mark Powell

collaborators

6 papers

math.GT2026

Smoothing 3-manifolds in 5-manifolds

Michelle Daher, Mark Powell

We show that every locally flat topological embedding of a 3-manifold in a smooth 5-manifold is homotopic, by a small homotopy, to a smooth embedding. We deduce that topologically…

math.GT2025

Spanning 3-discs in the 4-sphere pushed into the 5-disc

Mark Powell

I prove that any two smooth collections of spanning 3-discs for the trivial 2-link in $S^{4}$ become smoothly isotopic rel. boundary after pushing them into $D^{5}$ .

math.GT2025

Stably exotic 4-manifolds

Daniel Kasprowski, Mark Powell

A pair of closed, smooth $4$ -manifolds $M$ and $M^{'}$ are stably exotic if they are stably homeomorphic but not stably diffeomorphic, where stabilisation refers to connected sum with…

math.GT2025

Homotopy classification of $4$ -manifolds with $3$ -manifold fundamental group

Jonathan Hillman, Daniel Kasprowski, Mark Powell +1

We give a criterion on a group $I ¨ $ and a homomorphism $w : I ¨ \to C_{2}$ under which closed $4$ -manifolds with fundamental group $I ¨ $ and orientation character $w$ are classifie…

math.GT2025

Smoothly slice knots with smoothly non-approximable topological slice discs

Min Hoon Kim, Mark Powell

We construct infinitely many smoothly slice knots having topological slice discs that are non-approximable by smooth slice discs.

math.GT2025

Link concordance implies link homotopy

Maciej Borodzik, Mark Powell, Peter Teichner

We show that link concordance implies link homotopy for immersions of codimension at least two. As a consequence, we prove that every link $⊔^{r} S^{n} ↪ S^{n + 2}$ is…

Smoothing 3-manifolds in 5-manifolds

Spanning 3-discs in the 4-sphere pushed into the 5-disc

Stably exotic 4-manifolds

Homotopy classification of 4-manifolds with 3-manifold fundamental group

Smoothly slice knots with smoothly non-approximable topological slice discs

Link concordance implies link homotopy

Homotopy classification of $4$ -manifolds with $3$ -manifold fundamental group