Mahender Singh @ IISER Mohali

Welcome to the webpage!

Research Interests: Broad interests in topology, algebra, and their interplay. Particular topics include:

Equivariant algebraic topology, topological complexity, (co)homology theories.
Combinatorial and finite group theory, generalised braid groups, Artin and Coxeter groups.
Knot theory, mapping class groups of surfaces, solutions to the quantum Yang-Baxter equation.

News/Events:

Two PhD positions available. The candidates should already be selected for the PhD/Int-PhD program of IISER Mohali. Highly motivated IISER/IISc/IIT students willing for a direct PhD admission are also welcome.
One post-doctoral position available from August 2025 onwards.

Monograph submitted for publication:

Valeriy G. Bardakov, Mohamed Elhamdadi, and Mahender Singh, Yang-Baxter Equation and Related Algebraic Structures, (2024), 340 pages, 28 Figures and 06 Tables.

Preprints (available at arxiv):

(With D. Saraf), Second bounded cohomology of knot quandles, (2025), 15 pp.
(With N. K. Dhanwani, P. Kumar and T. K. Naik), Linear representations, crystallographic quotients, and twisted conjugacy of virtual Artin groups, (2024), 22 pp.
(With N. Rathee and A. Udeep), Representations of skew braces, (2024), 17 pp.
(With P. Kumar and A. Sanghi), Orderability of big mapping class groups, (2024), 22 pp.
(With B. Karmakar and D. Saraf), Beck modules over generalised Legendrian racks, (2023), 15 pp.
(With B. Karmakar and D. Saraf), Generalised Legendrian racks of Legendrian links, (2023), 15 pp.

Publications in Journals:

(With P. Kumar and A. Sanghi), Twisted Rokhlin property for mapping class groups, Proceedings of the Edinburgh Mathematical Society (2025), 23 pp.
(With N. K. Dhanwani and D. Saraf), Fundamental n-quandles of links are residually finite, Bulletin of the London Mathematical Society (2025), 18 pp.
(With B. Karmakar and D. Saraf), Automorphisms, cohomology and extensions of symmetric quandles, Homology Homotopy and Applications (2025), 20 pp.
(With N. K. Dhanwani), Finiteness of canonical quotients of Dehn quandles of surfaces, Journal of the Australian Mathematical Society 118 (2025), 317--334.
(With B. Karmakar and D. Saraf), Generalized (co)homology of symmetric quandles over homogeneous Beck modules, Journal of Pure and Applied Algebra 229 (2025), 107956, 31 pp.
(With N. Rathee), Relative Rota-Baxter groups and skew left braces, Forum Mathematicum 37 (2025), no. 3, 919--935.
(With P. Belwal and N. Rathee), Cohomology and extensions of relative Rota-Baxter groups, Journal of Geometry and Physics 207 (2025) 105353.
(With V. G. Bardakov and P. Kumar), Brunnian planar braids and simplicial groups, New York Journal of Mathematics 30 (2024) 1235--1263.
(With P. Belwal and N. Rathee), Schur multiplier and Schur covers of relative Rota-Baxter groups, Journal of Algebra 657 (2024), 327--362.
(With P. Kumar, T. K. Naik and N. Nanda), Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups, Journal of Pure and Applied Algebra 228 (2024),107713, 27 pp.
(With T. K. Naik and N. Nanda), Virtual planar braid groups and permutations, Journal of Group Theory 27 (2024), 443--483.
(With P. Kumar and T. K. Naik), Congruence subgroups and crystallographic quotients of small Coxeter groups, Forum Mathematicum 36 (2024), 193--213.
(With N. K. Dhanwani and H. Raundal), Dehn quandles of groups and orientable surfaces, Fundamenta Mathematicae, 263 (2023), 167--201.
(With T. K. Naik and N. Nanda), Structure and automorphisms of pure virtual twin groups, Monatshefte für Mathematik 202 (2023), 555--582.
(With N. K. Dhanwani and H. Raundal), Presentations of Dehn quandles, Journal of Algebra 636 (2023), 207-247.
(With M. Elhamdadi and B. Nunez), Enhancements of link colorings via idempotents of quandle rings, Journal of Pure and Applied Algebra 227 (2023) 107400, 16 pp.
(With M. Elhamdadi, B. Nunez and D. Swain), Idempotents, free products and quandle coverings, International Journal of Mathematics 34 (2023), 2350011, 27 pp.
(With V. G. Bardakov), A Wells type exact sequence for non-degenerate unitary solutions of the Yang-Baxter equation, Homology Homotopy and Applications 24(2) (2022), 31--51.
(With V. G. Bardakov and I. B. S. Passi), Zero-divisors and idempotents in quandle rings, Osaka Journal of Mathematics 59 (2022), 611--637.
(With V. G. Bardakov and T. R. Nasybullov), General constructions of biquandles and their symmetries, Journal of Pure and Applied Algebra 226 (2022), 106936, 40 pp.
(With H. Raundal and M. Singh), Orderability of link quandles, Proceedings of the Edinburgh Mathematical Society 64 (2021), 620--649.
(With V. G. Bardakov), Quandle cohomology, extensions and automorphisms, Journal of Algebra 585 (2021), 558--591.
(With T. K. Naik), Automorphisms of odd Coxeter groups, Monatshefte für Mathematik 195 (2021), 501--521.
(With N. Nanda), Alexander and Markov theorems for virtual doodles, New York Journal of Mathematics 27 (2021), 272--295.
(With T. K. Naik and N. Nanda), Some remarks on twin groups, Journal of Knot Theory and its Ramifications 29 (2020), 2042006, 14 pp.
(With V. G. Bardakov and M. V. Neshchadim), Exterior and symmetric (co)homology of groups, International Journal of Algebra and Computation 30 (2020), no. 8, 1577--1607.
(With T. K. Naik and N. Nanda), Conjugacy classes and automorphisms of twin groups, Forum Mathematicum 32 (2020), 1095--1108.
(With V. G. Bardakov and M. 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 P. Dey), Free actions of some compact groups on Milnor manifolds, Glasgow Mathematical Journal 61 (2019), 727--742.
(With V. G. Bardakov and M. Singh), Free quandles and knot quandles are residually finite, Proceedings of the American Mathematical Society 147 (2019), 3621--3633.
(With V. G. Bardakov and I. B. S. Passi), Quandle rings, Journal of Algebra and its Applications 18 (2019), 1950157, 23 pp.
(With V. G. Bardakov and T. R. Nasybullov), Automorphism groups of quandles and related groups, Monatshefte für Mathematik 189 (2019), 1--21.
(With Z. Blaszczyk and W. Marzantowicz), General Bourgin-Yang theorems, Topology and its Applications 249 (2018), 112--126.
(With V. G. Bardakov and M. V. Neshchadim), Automorphisms of pure braid groups, Monatshefte für Mathematik 187 (2018), 1--19.
(With M. C. Crabb), Some remarks on the parametrized Borsuk-Ulam theorem, Journal of Fixed Point Theory and Applications 20 (2018), 20:79.
(With Z. Blaszczyk and W. Marzantowicz), Equivariant maps between representation spheres, Bulletin of the Belgian Mathematical Society 24 (2017), 621--630.
(With V. G. Bardakov and P. Dey), Automorphism groups of quandles arising from groups, Monatshefte für Mathematik 184 (2017), 519--530.
(With V. G. Bardakov), Extensions and automorphisms of Lie algebras, Journal of Algebra and its Applications 16 (2017), 1750162, 15 pp.
Equivariant maps from Stiefel bundles to vector bundles, Proceedings of the Edinburgh Mathematical Society 60 (2017), 231--250.
(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.
Classification of flat connected quandles, Journal of Knot Theory and its Ramifications 25 (2016), 1650071, 8 pp.
(With D. de Mattos, P. L. Q. Pergher and E. L. dos Santos), Zero sets of equivariant maps from products of spheres to Euclidean spaces, Topology and its Applications 202 (2016), 7--20.
(With V. G. Bardakov and K. Gongopadhyay), Palindromic automorphisms of free groups, Journal of Algebra 438 (2015), 260--282.
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.
A note on the commutativity of inverse limit and orbit map, Mathematica Slovaca 61 (2011), 653--656.
Parametrized Borsuk-Ulam problem for projective space bundles, Fundamenta Mathematicae 211 (2011), 135--147.
(With I. B. S. Passi and M. K. Yadav), Automorphisms of abelian group extensions, Journal of Algebra 324 (2010), 820--830.
A simple proof of the Borsuk-Ulam theorem for $Z/p$-actions, Topology Proceedings 36 (2010), 249--253.
Orbit spaces of free involutions on products of two projective spaces, Results in Mathematics 57 (2010), 53--67.
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.
$Z/2$-actions on complexes with three non-trivial cells, Topology and its Applications 155 (2008), 965--971.

Conference Proceedings/Other Publications:

(With N. V. Abrosimov, V. G. Gorbounov, S. K. Nechaev and A. Y. Vesnin), Groups and quandles in low-dimensional topology, Siberian Electronic Mathematical Reports 18 (2021), pp. А30--А43.
(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.
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.

Books/Monographs Authored:

(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.

Books/Volumes Edited:

(With Y. Song and J. Wu), Algebraic Topology and Related Topics, Trends in Mathematics, Birkhaüser-Springer, (2019), ISBN 978-981-13-5741-1, ISSN 2297-0215, xv + 313 pp.

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