You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar
Speaker: Yıldıray Ozan (ODTÜ)
“Liftable homeomorphisms of finite abelian p-group regular branched covers over the 2-sphere and the projective plane”
Abstract: This talk mainly is based our work joint with F. Atalan and E. Medetoğulları.
In 2017 Ghaswala and Winarski classified finite cyclic regular branched coverings of the 2-sphere, where every homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface, answering a question of Birman and Hilden. In this talk, we will present generalizations of this result in two directions. First, we will replace finite cyclic groups with finite abelian p-groups. Second, we will replace the base surface with the real projective plane.
The main tool is the algebraic characterization of such coverings in terms of the automorphism groups of these finite abelian p-groups. Due to computational insufficiencies we have complete results only for groups of rank 1 and 2.
In particular, we prove that for a regular branched $A$-covering $pi:Sigmarightarrow S^2$, where $A={mathbb Z}_{p^r}times{mathbb Z}_{p^t}, 1leq rleq t$, all homeomorphisms $f:S^2 to S^2$ lift to those of $Sigma$, if and only if $t=r$ or $t=r+1$ and $p=3$.
If time permits we will also present some applications to automorphisms of Riemann surfaces.
Date: 12 February 2021, Friday
Time: 15:40 (GMT+3)
Place: Zoom
This is an online seminar. To request the event link, please send a message to sertoz@bilkent.edu.tr