Mahender Singh

PIC

Subject Area: Topology and Groups

Background and Research Interests

My main areas of interest are algebraic topology, group theory, and related topics.

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 structures on smooth manifolds.

Group theory is closely related to transformation groups due to abundance of topological spaces admitting non-trivial group actions. It is well known that; a finite group acts freely on a sphere if and only if it has periodic cohomology and each element of order two is central. The subject of cohomology of groups is a bridge between group theory and topology. I am interested in applications of cohomology of groups in the study of automorphisms of finite groups. I am also interested in cohomology of groups as an independent topic.

Select Publications

  1. Free 2-rank of symmetry of products of Milnor manifolds, Homology Homotopy and Applications (2013) (to appear).
  2. Symmetric continuous cohomology of topological groups, Homology Homotopy and Applications 15 (2013) 279-302.
  3. Cohomology algebra of orbit spaces of free involutions on lens spaces, Journal of the Mathematical Society of Japan 65 (2013) 1038-1061.
  4. Parametrized Borsuk-Ulam problem for projective space bundles, Fundamenta Mathematicae 211 (2011) 135-147.
  5. (with I. B. S. Passi and M. K. Yadav), Automorphisms of abelian group extensions, Journal of Algebra 324 (2010) 820-830.
  6. Fixed points of circle actions on spaces with rational cohomology of Sn S2n S3n or P2(n) S3n, Archiv der Mathematik 92 (2009) 174-183.