Can I read Birman-Hilden theory for 3-manifolds on EtoBox?

Birman-Hilden theory for 3-manifolds by Lucas, Trent is a scholarly article available to read on EtoBox.

What is Birman-Hilden theory for 3-manifolds about?

Given a branched cover of manifolds, one can lift homeomorphisms along the cover to obtain a (virtual) homomorphism between mapping class groups. Following a question of Margalit-Winarski, we study the injectivity of this lifting map in the case of $3$-manifolds. We show that in contrast to the case of surfaces, the lifting map is generally not injective for most regular branched covers of $3$-manifolds. This includes the double cover of $S^3$ branched over the unlink, which generalizes the hyperelliptic branched cover of $S^2$. In this case, we find a finite normal generating set for the kernel of the lifting map.

Author

Lucas, Trent

Published

2024

Language

EN