Clayton McDonald

collaborators

4 papers

math.GT2026

An $S^{2} \times S^{2}$ embedding

Clayton McDonald

In this note, we give a positive answer to K3 problem 4.28b, giving the first examples of homology 3-spheres that embed smoothly in $S^{2} \times S^{2}$ but not $S^{4}$ .

math.GT2026

Cobordism-equivalence for codimension-one submanifolds

Stefan Friedl, Tobias Hirsch, Clayton McDonald +2

We show that two hypersurfaces in a manifold are related by a sequence of embedded cobordisms if and only if they represent the same homology class. By applying handle decompositio…

math.GT2026

A note on smoothly slice links in $S^{2} \times S^{2}$

Marco Marengon, Clayton McDonald

We give an alternative proof of a result of Miyazaki and Yasuhara that there exists links that are not smoothly slice in $S^{2} \times S^{2}$ . We discuss potential applications to the…

math.GT2024

Smoothly slice links in $CP^{2} # CP^{2}$

Marco Marengon, Clayton McDonald

We show that there exists a link with 2 components which is not smoothly slice in $CP^{2} # CP^{2}$ . By contrast, it is well-known that every knot (i.e.,…

An S2×S2 embedding

Cobordism-equivalence for codimension-one submanifolds

A note on smoothly slice links in S2×S2

Smoothly slice links in CP2#CP2

An $S^{2} \times S^{2}$ embedding

A note on smoothly slice links in $S^{2} \times S^{2}$

Smoothly slice links in $CP^{2} # CP^{2}$