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SEMINAR: Groups and Combinatorics Seminar: The superelliptic covers and the lifting mapping class group

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Today's date is Friday, March 29, 2024
Groups and Combinatorics Seminar: The superelliptic covers and the lifting mapping class group Other events...
Time and place: 16:00 Friday 15 April in Weatherburn LT

Speaker: Ty Ghaswala (University of Waterloo)

Title: The superelliptic covers and the lifting mapping class group

Abstract: Given a finite sheeted (possibly branched) covering space over a surface, one can ask the following question:  Which homeomorphisms of the base space lift to homeomorphisms of the total space?  If we take the quotient of this question by isotopy, it becomes a much more interesting one:  What can we say about the subgroup of the mapping class group of the base space that consists of isotopy classes of homeomorphisms that lift to the total space?  This subgroup is the lifting mapping class group.

This question was completely answered by Birman and Hilden when the deck group is the two element group generated by a fixed hyperelliptic involution.  In this case, everything lifts.  Interestingly, this does not happen in general.

In this talk, I will give an introduction to the mapping class group of a surface and a history of this lifting problem.  I will then focus on the algebraic structure of the lifting mapping class group in the case of the superelliptic covers, which are $n$-sheeted generalisations of the 2-sheeted covering spaces studied by Birman and Hilden.  Time permitting, I will outline some interesting questions that arise from this work.

This is joint work with Rebecca Winarski.
Contact Tomasz Popiel <[email protected]>
Start Fri, 15 Apr 2016 16:00
End Fri, 15 Apr 2016 17:00
Submitted by Tomasz Popiel <[email protected]>
Last Updated Mon, 11 Apr 2016 13:19
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