24 citations · 182 across the 31 of their papers we have counts for
35 papers
Virtual planar braid groups and permutations
Tushar Kanta Naik, Neha Nanda, Mahender Singh
Twin groups and virtual twin groups are planar analogues of braid groups and virtual braid groups, respectively. These groups play the role of braid groups in the Alexander-Markov…
Dehn quandles of groups and orientable surfaces
Neeraj K. Dhanwani, Hitesh Raundal, Mahender Singh
Unifying various constructions of quandles including Coxeter quandles, free quandles, knot quandles of prime knots and Dehn quandles of orientable surfaces, we introduce Dehn quand…
A Wells type exact sequence for non-degenerate unitary solutions of the Yang--Baxter equation
Valeriy Bardakov, Mahender Singh
Cycle sets are known to give non-degenerate unitary solutions of the Yang--Baxter equation and linear cycle sets are enriched versions of these algebraic systems. The paper explore…
Alexander and Markov theorems for virtual doodles
Neha Nanda, Mahender Singh
Study of certain isotopy classes of a finite collection of immersed circles without triple or higher intersections on closed oriented surfaces can be thought of as a planar analogu…
Quandle cohomology, extensions and automorphisms
Valeriy Bardakov, Mahender Singh
The paper establishes new relationship between cohomology, extensions and automorphisms of quandles. We derive a four term exact sequence relating quandle 1-cocycles, second quandl…
Automorphisms of odd Coxeter groups
Tushar Kanta Naik, Mahender Singh
An odd Coxeter group is one which admits a Coxeter system for which all the exponents are either odd or infinity. The paper investigates the family of odd Coxe…
Zero-divisors and idempotents in quandle rings
Valeriy G. Bardakov, Inder Bir S. Passi, Mahender Singh
The paper develops further the theory of quandle rings which was introduced by the authors in a recent work. Orderability of quandles is defined and many interesting examples of or…
Some remarks on twin groups
Tushar Kanta Naik, Neha Nanda, Mahender Singh
The twin group is a right angled Coxeter group generated by involutions and having only far commutativity relations. These groups can be thought of as planar analogues…
General constructions of biquandles and their symmetries
Valeriy Bardakov, Timur Nasybullov, Mahender Singh
Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set-theor…
Conjugacy classes and automorphisms of twin groups
Tushar Kanta Naik, Neha Nanda, Mahender Singh
The twin group is a right angled Coxeter group generated by involutions and the pure twin group is the kernel of the natural surjection from onto the symme…
Structural aspects of twin and pure twin groups
Valeriy Bardakov, Mahender Singh, Andrei Vesnin
The twin group is a Coxeter group generated by involutions and the pure twin group is the kernel of the natural surjection of onto the symmetric group on $…
Exterior and symmetric (co)homology of groups
Valeriy G. Bardakov, Mikhail V. Neshchadim, Mahender Singh
The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite g…
Derivations of quandles
Neha Nanda, Mahender Singh, Manpreet Singh
The aim of this paper is to propose a theory of derivations for quandles. Given a quandle admitting an action by a quandle , derivations from to are introduced as tw…
Free actions of some compact groups on Milnor manifolds
Pinka Dey, Mahender Singh
In this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the or…
Some remarks on the parametrized Borsuk-Ulam theorem
Michael Crabb, Mahender Singh
Given a locally trivial fibre bundle (with fibres and base finite complexes), an orthogonal real line bundle over and a real vector bundle over , we consid…
Quandle rings
Valeriy G. Bardakov, Inder Bir Singh Passi, Mahender Singh
In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated…
Automorphism groups of quandles and related groups
Valeriy Bardakov, Timur Nasybullov, Mahender Singh
In this paper we study different questions concerning automorphisms of quandles. For a conjugation quandle of a group we determine several subgroups of ${\rm…
Automorphisms of pure braid Groups
Valeriy G. Bardakov, Mikhail V. Neshchadim, Mahender Singh
In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for , $\Aut(P_n)$ is generated by the subgroup $\Aut_c(P_n)$ of cen…
Equivariant maps between representation spheres
Zbigniew Błaszczyk, Wacław Marzantowicz, Mahender Singh
Let be a compact Lie group. We prove that if and are orthogonal -representations such that , then a -equivariant map exists provide…
Automorphism groups of quandles arising from groups
Valeriy G. Bardakov, Pinka Dey, Mahender Singh
Let be a group and $φ\in \Aut(G)$. Then the set equipped with the binary operation gives a quandle structure on , denoted by $\Alex(G, φ)$ and called t…
General Bourgin-Yang theorems
Zbigniew Błaszczyk, Wacław Marzantowicz, Mahender Singh
We describe a unified approach to estimating the dimension of for any -equivariant map and any closed -invariant subset in terms…
Extensions and automorphisms of Lie algebras
Valeriy G. Bardakov, Mahender Singh
Let be a short exact sequence of Lie algebras over a field , where is abelian. We show that the obstruction for a pair of automorphisms in $\Aut(…
Palindromic Automorphisms of Free Nilpotent Groups
Valeriy G. Bardakov, Krishnendu Gongopadhyay, Mikhail V. Neshchadim +1
In this paper, we initiate the study of palindromic automorphisms of groups that are free in some variety. More specifically, we define palindromic automorphisms of free nilpotent…
Some Problems on Knots, Braids, and Automorphism Groups
Valeriy G. Bardakov, Krishnendu Gongopadhyay, Mahender Singh +2
We present and discuss some open problems formulated by participants of the International Workshop "Knots, Braids, and Auto\-mor\-phism Groups" held in Novosibirsk, 2014. Problems…