My interests are broadly in topology and algebra. Particularly, I work on problems related to compact group actions on manifolds, equivariant maps, braid groups, knot theory, automorphisms and cohomology of groups and related algebraic structures.
Algebraic topology can be described as the study of topological spaces by means of algebraic objects associated to them. I am interested in group actions on manifolds, equivariant maps, free rank, index theory, and recently topological complexity.
Group theory is closely related to transformation groups due to abundance of topological spaces admitting non-trivial group actions. I am interested in cohomology of groups, automorphisms and conjugacy classes in generalized braid groups and Coxeter groups
Recently, I ventured into knot theory with a focus on algebraic aspects of the subject. I have been working towards finding newer properties of important knot invariants like quandles. These objects give strong invariants of knots and appear in diverse areas of mathematics like group theory, Yang-Baxter equations, Hopf Algebras and Symmetric spaces, to name a few.
- (With V.G. Bardakov and Manpreet Singh), Link quandles are residually finite, Monatshefte für Mathematik 191 (2020), 679--690.
- (With V.G. Bardakov and A.Y. Vesnin), Structural aspects of twin and pure twin groups, Geometriae Dedicata 203 (2019), 135--154.
- (With V.G. Bardakov and Manpreet Singh), Free quandles and knot quandles are residually finite, Proceedings of the American Mathematical Society 147 (2019), 3621--3633.
- (With V.G. Bardakov and T.R. Nasybullov), Automorphism groups of quandles and related groups, Monatshefte fuer Mathematik 189 (2019), 1--21.
- (With I.B.S. Passi and M.K. Yadav), Automorphisms of Finite Groups, Springer Monographs in Mathematics, Springer, (2018), ISBN 978-981-13-2894-7, ISSN 1439-7382, xix + 217 pp.
- (With V.G. Bardakov and M.V. Neshchadim), Automorphisms of pure braid
groups, Monatshefte fuer Mathematik 187 (2018), 1--19.