Krishnendu Gongopadhyay

activity

20052026

most citedPalindromic Automorphisms of Free Groups

10 citations · 55 across the 60 of their papers we have counts for

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30 papers · 1 filter

math.GT2026

Trace Coordinates and Local Fenchel--Nielsen Parameters in Real Hyperbolic 5-Space

Krishnendu Gongopadhyay, Sagar B. Kalane, Abhishek Mukherjee

We study representations of fundamental groups of closed orientable surfaces into $\mathrm{SL}(2,\mathbb{H})$, whose projectivization $\mathrm{PSL}(2,\mathbb{H})$ is the group…

math.GT2026

Combinatorial Structure of Inert and Ambiguous Classes in Modular Group

Debattam Das, Krishnendu Gongopadhyay, Khushi Mishra

We study inert, and ambiguous conjugacy classes in the modular group $PSL (2, Z)$ from a purely combinatorial perspective. Using word length in the free product rep…

math.GT2025

Thurston's asymmetric metric on Margulis spacetimes

Krishnendu Gongopadhyay, Neelanjan Mondal

In this article, we extend Thurston's asymmetric metric and the associated Finsler norm, originally defined for Teichmüller space, to the setting of Margulis spacetimes. We also es…

math.GT2025

Functorial Free Group from Anosov Representations on Bundles

Krishnendu Gongopadhyay, Tathagata Nayak

Let $ρ : Γ \to G$ be an Anosov representation, with $Γ$ a word hyperbolic group and $G$ a semisimple Lie group. Previous works (Guichard--Wienhard, Kapovich--Leeb--Porti, and Carvaja…

math.GT2025

On the domination of surface-group representations in $PU (2, 1)$

Pabitra Barman, Krishnendu Gongopadhyay

This article explores surface-group representations into the complex hyperbolic group $PU (2, 1)$ and presents domination results for a special class of representations call…

math.GT2025

Equidistant Hypersurfaces Of The Complex Bidisk $H_{C}^{2} \times H_{C}^{2}$

Krishnendu Gongopadhyay, Lokenath Kundu, Aditya Tiwari

We consider the isometries of the complex hyperbolic bidisk, that is, the product space $H_{C}^{2} \times H_{C}^{2}$ , where each factor $ \mathbb{H…

math.GT2024

On Character Variety of Anosov Representations

Krishnendu Gongopadhyay, Tathagata Nayak

Let $Γ$ be the fundamental group of a $k$ -punctured, $k \geq 0$ , closed connected orientable surface of genus $g \geq 2$ . We show that the character variety of the $(Q^{+}, Q^{-})$ -Ano…

math.GT2024

Algebraic characterization of reversibility in the quaternionic Möbius group

Krishnendu Gongopadhyay, Tejbir Lohan, Abhishek Mukherjee

An element of a group is called \emph{reversible} if it is conjugate to its inverse. While reversibility in the quaternionic Möbius group $PSL (2, H)$ has tradition…

math.GT2020

On some decompositions of the 3-strand Singular Braid Group

Krishnendu Gongopadhyay, Tatyana A. Kozlovskaya, Oleg V. Mamonov

Let $S B_{n}$ be the singular braid group generated by braid generators $σ_{i}$ and singular braid generators $τ_{i}$ , $1 \leq i \leq n - 1$ . Let $S T_{n}$ denote the group that is the kernel…

math.GT2019★ 1 cited

Local coordinates for complex and quaternionic hyperbolic pairs

Krishnendu Gongopadhyay, Sagar B. Kalane

Let $G (n) = Sp (n, 1)$ or $SU (n, 1)$ . We classify conjugation orbits of generic pairs of loxodromic elements in $G (n)$ . Such pairs, called `non-singular', were introduced by…

math.GT2019

Reversible Quaternionic Hyperbolic Isometries

Sushil Bhunia, Krishnendu Gongopadhyay

Let $G$ be a group. An element $g$ in $G$ is called reversible if it is conjugate to $g^{- 1}$ within $G$ , and called strongly reversible if it is conjugate to its inverse by an ord…

math.GT2018

Discreteness Of Hyperbolic Isometries by Test Maps

Krishnendu Gongopadhyay, Abhishek Mukherjee, Devendra Tiwari

Let $F = R$ , $C$ or $H$ . Let $H_{F}^{n}$ denote the $n$ -dimensional $F$ -hyperbolic space. Let $U (n, 1; F)$ be the lin…

math.GT2018

On discreteness of subgroups of quaternionic hyperbolic isometries

Krishnendu Gongopadhyay, Mukund Madhav Mishra, Devendra Tiwari

Let $H_{H}^{n}$ denote the $n$ -dimensional quaternionic hyperbolic space. The linear group $Sp (n, 1)$ acts by the isometries of $H_{H}^{n}$ . A sub…

math.GT2018

On generalized Jørgensen inequality in infinite dimension

Krishnendu Gongopadhyay

In New York J. Math. 17 (2011), 41--49, Li has obtained an analogue of the Jørgensen inequality in the infinite-dimensional Möbius group. We show that this inequality is strict.

math.GT2018

Commutator Subgroups of Singular Braid Groups

Soumya Dey, Krishnendu Gongopadhyay

The singular braids with $n$ strands, $n \geq 3$ , were introduced independently by Baez and Birman. It is known that the monoid formed by the singular braids is embedded in a group…

math.GT2018

Commutator Subgroups of Twin Groups and Grothendieck's Cartographical Groups

Soumya Dey, Krishnendu Gongopadhyay

Let $T W_{n}$ be the twin group on $n$ arcs, $n \geq 2$ . The group $T W_{m + 2}$ is isomorphic to Grothendieck's $m$ -dimensional cartographical group $C_{m}$ , $m \geq 1$ . In this…

math.GT2018

Commutator Subgroups of Virtual and Welded Braid Groups

Valeriy G. Bardakov, Krishnendu Gongopadhyay, Mikhail V. Neshchadim

Let $V B_{n}$ , resp. $W B_{n}$ denote the virtual, resp. welded, braid group on $n$ strands. We study their commutator subgroups $V B_{n}^{'} = [V B_{n}, V B_{n}]$ and, $W B_{n}^{'} = [W B_{n}, W B_{n}]$ respec…

math.GT2018

On Conjugation orbits of semisimple pairs in rank one

Krishnendu Gongopadhyay, Sagar B. Kalane

We consider Lie groups $SU (n, 1)$ and $Sp (n, 1)$ that act as the isometries of the complex and quaternionic hyperbolic spaces respectively. We classify pairs of semisimpl…

math.GT2017

Quaternionic Hyperbolic Fenchel-Nielsen Coordinates

Krishnendu Gongopadhyay, Sagar B. Kalane

Let $S p (2, 1)$ be the isometry group of the quaternionic hyperbolic plane $H_{H}^{2}$ . An element $g$ in $S p (2, 1)$ is `hyperbolic' if it fixes exactly two points on th…

math.GT2017

Test map and Discreteness in SL(2, $H$ )

Krishnendu Gongopadhyay, Abhishek Mukherjee, Sujit Kumar Sardar

Let SL(2, $H$ ) be the group of $2 \times 2$ quaternionic matrices $A = (a c b d)$ with quaternionic determinant $det A = ∣ a d - a c a^{- 1} b ∣ = 1$ .…

math.GT2017

Conjugation Orbits of Loxodromic Pairs in SU(n,1)

Krishnendu Gongopadhyay, Shiv Parsad

Let $H_{C}^{n}$ be the $n$ -dimensional complex hyperbolic space and $SU (n, 1)$ be the (holomorphic) isometry group. An element $g$ in $SU (n, 1)$ is called lox…

math.GT2017

Commutator Subgroups of Welded Braid Groups

Soumya Dey, Krishnendu Gongopadhyay

Let $W B_{n}$ be the welded (or loop) braid group on n strands, $n \geq 3$ . We investigate commutator subgroup of $W B_{n}$ . We prove that the commutator subgroup $W B_{n}^{'}$ is finitely gen…

math.GT2015

Decomposition of complex hyperbolic isometries by involutions

Krishnendu Gongopadhyay, Cigole Thomas

A $k$ -reflection of the $n$ -dimensional complex hyperbolic space ${\rm H}_{\C}^n$ is an element in $U (n, 1)$ with negative type eigenvalue $λ$ , $∣ λ ∣ = 1$ , of multiplicity $k + 1$ …

math.GT2015★ 5 cited

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…

Trace Coordinates and Local Fenchel--Nielsen Parameters in Real Hyperbolic 5-Space

Combinatorial Structure of Inert and Ambiguous Classes in Modular Group

Thurston's asymmetric metric on Margulis spacetimes

Functorial Free Group from Anosov Representations on Bundles

On the domination of surface-group representations in PU(2,1)

Equidistant Hypersurfaces Of The Complex Bidisk HC2​×HC2​

On Character Variety of Anosov Representations

Algebraic characterization of reversibility in the quaternionic Möbius group

On some decompositions of the 3-strand Singular Braid Group

Local coordinates for complex and quaternionic hyperbolic pairs

Reversible Quaternionic Hyperbolic Isometries

Discreteness Of Hyperbolic Isometries by Test Maps

On discreteness of subgroups of quaternionic hyperbolic isometries

On generalized Jørgensen inequality in infinite dimension

Commutator Subgroups of Singular Braid Groups

Commutator Subgroups of Twin Groups and Grothendieck's Cartographical Groups

Commutator Subgroups of Virtual and Welded Braid Groups

On Conjugation orbits of semisimple pairs in rank one

Quaternionic Hyperbolic Fenchel-Nielsen Coordinates

Test map and Discreteness in SL(2, H)

Conjugation Orbits of Loxodromic Pairs in SU(n,1)

Commutator Subgroups of Welded Braid Groups

Decomposition of complex hyperbolic isometries by involutions

Some Problems on Knots, Braids, and Automorphism Groups

On the domination of surface-group representations in $PU (2, 1)$

Equidistant Hypersurfaces Of The Complex Bidisk $H_{C}^{2} \times H_{C}^{2}$

Test map and Discreteness in SL(2, $H$ )