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A note on normal generation and the first -betti number
Sam P. Fisher, Yash Lodha
In , Osin and Thom conjectured that the first -Betti number of a torsion-free discrete group is bounded above by the normal rank of the group minus one. The conjectur…
On Ulam widths of finitely presented infinite simple groups
James Hyde, Yash Lodha
A fundamental notion in group theory, which originates in an article of Ulam and von Neumann from is uniform simplicity. A group is said to be -uniformly simple for $…
The Wiegold problem and free products of left-orderable groups
Lvzhou Chen, Yash Lodha
A group has normal rank (or weight) greater than one if no single element normally generates the group. The Wiegold problem from 1976 asks about the existence of a finitely generat…
Generic torsion-free groups and Rubin actions
Thomas Koberda, Yash Lodha
We use model theoretic forcing to prove that a generic countable torsion-free group does not admit any nontrivial locally moving action on a Hausdorff topological space, and yet ad…
An algebraic criterion for the vanishing of bounded cohomology
Caterina Campagnolo, Francesco Fournier-Facio, Yash Lodha +1
We prove the vanishing of bounded cohomology with separable dual coefficients for many groups of interest in geometry, dynamics, and algebra. These include compactly supported stru…
On some algebraic and analytic properties of the finitely generated simple left orderable groups
Pawel Aleksander Fedorynski, Yash Lodha
In Hyde and the second author constructed the first family of finitely generated, simple, left orderable groups. We prove that these groups are not finitely presentable, non…