Research


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 quandles.

Monographs:
Edited Volumes:
Preprints:
    1. (With V.G. Bardakov and M.V. Neshchadim), Exterior and symmetric (co)homology of groups, (2018), preprint.
    2. (With V.G. Bardakov and A.Y. Vesnin), Structural aspects of twin and pure twin groups, (2018), preprint.
    3. (With Neha Nanda and Manpreet Singh), Knot invariants from derivations of quandles, (2018), preprint.
    Publications in Journals:
    1. (With V.G. Bardakov and Manpreet Singh), Free quandles and knot quandles are residually finite, Proceedings of the American Mathematical Society (2018).
    2. (With Pinka Dey), Free actions of some compact groups on Milnor manifoldsGlasgow Mathematical Journal (2018).
    3. (With V.G. Bardakov and T.R. Nasybullov), Automorphism groups of quandles and related groupsMonatshefte für Mathematik (2018).
    4. (With V.G. Bardakov and  I.B.S. Passi), Quandle ringsJournal of Algebra and its Applications (2019), 1950157, 23 pp.
    5. (With Z. Blaszczyk and W. Marzantowicz), General Bourgin-Yang theoremsTopology and its Applications 249 (2018), 112--126.
    6. (With M.C. Crabb), Some remarks on the parametrized Borsuk-Ulam theorem, Journal of Fixed Point Theory and Applications 20 (2018), 20:79.
    7. (With V.G. Bardakov and M.V. Neshchadim)Automorphisms of pure braid groups,  Monatshefte für Mathematik 187 (2018), 1--19.
    8. (With Z. Blaszczyk and W. Marzantowicz), Equivariant maps between representation spheresBulletin of the Belgian Mathematical Society 24 (2017), 621--630.
    9. (With V.G. Bardakov and Pinka Dey), Automorphism groups of quandles arising from groupsMonatshefte für Mathematik 184 (2017), 519--530.
    10. (With V.G. Bardakov), Extensions and automorphisms of Lie algebrasJournal of Algebra and its Applications 16 (2017), 1750162, 15 pp.
    11. Equivariant maps from Stiefel bundles to vector bundlesProceedings of the Edinburgh Mathematical Society 60 (2017), 231--250.
    12. (With V.G. Bardakov, K. Gongopadhyay and M.V. Neshchadim), Palindromic automorphisms of free nilpotent groups, Journal of Pure and Applied Algebra 221 (2017), 316--338.
    13. Classification of flat connected quandlesJournal of Knot Theory and its Ramifications 25 (2016), 1650071, 8 pp.
    14. (With D. de Mattos, P.L.Q. Pergher and E.L. dos Santos), Zero sets of equivariant maps from products of spheres to Euclidean spacesTopology and its Applications 202 (2016), 7--20.
    15. (With V.G. Bardakov and K. Gongopadhyay), Palindromic automorphisms of free groups, Journal of Algebra 438 (2015), 260--282.
    16. Free 2-rank of symmetry of products of Milnor manifolds, Homology Homotopy and Applications 16 (2014), 65--81.
    17. Cohomology algebra of orbit spaces of free involutions on lens spaces, Journal of the Mathematical Society of Japan 65 (2013), 1055--1078.
    18. Symmetric continuous cohomology of topological groups, Homology Homotopy and Applications 15 (2013), 279--302.
    19. A note on the commutativity of inverse limit and orbit map, Mathematica Slovaca 61 (2011), 653--656.
    20. Parametrized Borsuk-Ulam problem for projective space bundles, Fundamenta Mathematicae 211 (2011), 135--147.
    21. (With I.B.S. Passi and M.K. Yadav), Automorphisms of abelian group extensions, Journal of Algebra 324 (2010), 820--830.
    22. A simple proof of the Borsuk-Ulam theorem for $Z/p$-actions, Topology Proceedings 36 (2010), 249--253.
    23. Orbit spaces of free involutions on products of two projective spaces, Results in Mathematics 57 (2010), 53--67.
    24. Fixed points of circle actions on spaces with rational cohomology of $S^{n} V S^{2n} V S^{3n}$ or $P^2(n) V S^{3n}$, Archiv der Mathematik 92 (2009), 174--183.
    25. $Z/2$-actions on complexes with three non-trivial cells, Topology and its Applications 155 (2008), 965--971.
    Publications in Conference Proceedings:
    1. (With V.G. Bardakov, K. Gongopadhyay, A.Y. Vesnin and J. Wu), Some problems on knots, braids and automorphism groups (Proceedings of a conference held at Sobolev Institute of Mathematics, Novosibirsk)Siberian Electronic Mathematical Reports 12 (2015), 394--405.
    2. Involutions on cohomology lens spaces and projective spaces (Proceedings of a conference held at Research Institute for Mathematical Sciences, Kyoto),  RIMS Kokyuroku 1670 (2009), 15--24.