Dr. Mahender Singh
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Topology and Groups
My research interests are broadly in topology and algebra. Particularly, I work on problems related to compact group actions on manifolds, equivariant maps, braid groups, automorphisms and cohomology of groups and quandles.
Algebraic topology can be described as the study of topological spaces by means of algebraic objects associated to them. This leads to a rich interaction between several areas of mathematics including topology, group theory and geometry, to name a few. Particularly, I am interested in group actions on manifolds, equivariant maps, free rank, index theory, cohomological dimension and recently topological complexity.
Group theory is closely related to transformation groups due to abundance of topological spaces admitting non-trivial group actions. The cohomology of groups is a subject which straddles algebra and topology. I am interested in applications of cohomology of groups in the study of automorphisms of finite groups. Recently, I got interested in the theory of quandles, which are algebraic objects used in the study of knots. Particularly, I have been thinking on automorphisms and cohomology of quandles.
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