Rajesh Dey

Ph.D. Student

Indian Institute of Science Education and Research Bhopal.

Research area: Mapping Class Groups of Surfaces.

E-mail: rajesh17@iiserb.ac.in, rdeymath@gmail.com

About Me

I am pursuing the final year of my PhD at IISER Bhopal. My advisor is Prof. Kashyap Rajeevsarathy.

Research Interests

My research interest lies in studying finite subgroups of mapping class groups of closed, orientable surfaces. In particular, subgroups of mapping class groups that are either isomorphic to an alternating group (simple group) or an extension of a finite cyclic group by an alternating group (i.e., the groups whose alternating quotient is cyclic). The motivation behind choosing these subgroups is the problem of the liftability of periodic mapping classes under simple covers. Using the Birman-Hilden theory, one can determine torsion elements of liftable mapping class groups under finite-sheeted alternating covers by classifying these subgroups (up to some equivalence). In this context, I am currently pursuing the following problems.

Up to some equivalence, classify the subgroups of mapping class groups that are either isomorphic to an alternating group or an extension of a finite cyclic group by an alternating group.
Find a realizable bound on the orders of a sub-family (other than alternating and symmetric groups, as they are known) of these subgroups of the mapping class groups.
Characterize the periodic mapping classes, up to some equivalence, that lift under finite-sheeted alternating covers.
Characterize the reducible (or pseudo-Anosov) mapping classes, up to some equivalence, that lift under finite-sheeted alternating covers.

Preprints

Alternating and symmetric actions on surfaces, joint work with Dr. Kashyap Rajeevsarathy, arXiv link: arXiv:2310.06550, submitted.

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