Corey Bregman

activity

20242026

collaborators

6 papers

math.GT2026

Isotopy and equivalence of knots in 3-manifolds

Paolo Aceto, Corey Bregman, Christopher W. Davis +2

We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irred…

math.GT2026

The prime decomposition fibre sequence for moduli spaces of reducible 3-manifolds

Rachael Boyd, Corey Bregman, Jan Steinebrunner

We study the moduli space $B Diff^{+} (M)$ , for $M$ a reducible, oriented 3-manifold with irreducible prime factors $P_{1}, \dots, P_{n}$ . A programme of CÃ©sar de SÃ¡-Rourke, Hend…

math.GT2025

The embedding space of a Hopf link

Rachael Boyd, Corey Bregman

We study the unparametrised smooth embedding space of a Hopf link in $R^{3}$ , and prove that it is homotopy equivalent to the closed 3-manifold $S^{3} / Q_{8}$ . As an int…

math.GT2025

Extending families of homeomorphisms over 4-dimensional handlebodies

Rachael Boyd, Corey Bregman, Jan Steinebrunner

Let $H_{g}$ denote the 4-dimensional handlebody of genus $g$ and $U_{g}$ its boundary. We show that for all $g \geq 0$ the map from $B H o m eo (H_{g})$ to $B H o m eo (U_{g})$ induced by restricti…

math.GT2025

Embedding spaces of split links

Rachael Boyd, Corey Bregman

We study the homotopy type of the space $E (L)$ of unparametrised embeddings of a split link $L = L_{1} ⊔ \dots ⊔ L_{n}$ in $R^{3}$ . Our main result is a simple descripti…

math.GT2024

CAT(0) geometry of complex curve complements and families

Corey Bregman, Anatoly Libgober, Kejia Zhu

Motivated by the question of whether braid groups are CAT(0), we investigate the CAT(0) behavior of fundamental groups of plane curve complements and certain universal families. If…