5 papers
Linear representations, crystallographic quotients, and twisted conjugacy of virtual Artin groups
Neeraj Kumar Dhanwani, Pravin Kumar, Tushar Kanta Naik +1
Virtual Artin groups were recently introduced by Bellingeri, Paris, and Thiel as broad generalizations of the well-known virtual braid groups. For each Coxeter graph , they defi…
Orderability of big mapping class groups
Pravin Kumar, Apeksha Sanghi, Mahender Singh
We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves t…
Twisted Rokhlin property for mapping class groups
Pravin Kumar, Apeksha Sanghi, Mahender Singh
In this paper, generalising the idea of the Rokhlin property, we explore the concept of the twisted Rokhlin property of topological groups. A topological group is said to exhibit t…
Brunnian planar braids and simplicial groups
Valeriy G. Bardakov, Pravin Kumar, Mahender Singh
Twin groups are planar analogues of Artin braid groups and play a crucial role in the Alexander-Markov correspondence for the isotopy classes of immersed circles on the 2-sphere wi…
Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups
Pravin Kumar, Tushar Kanta Naik, Neha Nanda +1
The virtual braid group , the virtual twin group and the virtual triplet group are extensions of the symmetric group , which are motivated by the Alexander…