IISER Mohali, Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306

Dr. Mahender Singh
Assistant Professor , Mathematical Sciences

Email mahender(AT)iisermohali.ac.in
Phone +91 172 2293135
Fax +91 172 2240266
Personal Page My Webpage                       
Research Area
Topology and Groups
Research Focus

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.

 


Selected Publications

  • (With V.G. Bardakov and P. Dey), Automorphism groups of quandles arising from groups, Monatshefte fuer Mathematik (2017), DOI: 10.1007/s00605-017-1073-7.
  • Equivariant maps from Stiefel bundles to vector bundles, Proceedings of the Edinburgh Mathematical Society 60 (2016), 231--250.
  • Free 2-rank of symmetry of products of Milnor manifolds, Homology Homotopy and Applications 16 (2014), 65--81.
  • Cohomology algebra of orbit spaces of free involutions on lens spaces, Journal of the Mathematical Society of Japan 65 (2013), 1055--1078.
  • Symmetric continuous cohomology of topological groups, Homology Homotopy and Applications 15 (2013), 279--302.
  • Parametrized Borsuk-Ulam problem for projective space bundles, Fundamenta Mathematicae, 211 (2011), 135-147.

 

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