arXiv subjects

Chaitanya Ambi

Publications and source records attributed to Chaitanya Ambi.

4 recordsLinked to original sources

arXiv2023

Two Applications of Topological Fixed Point Theory

We give a new proof of Cartan's fixed point theorem using topological fixed point theory. For an odd dimensional, simply connected and complete manifold having non-positive curvature, we further prove that every isometry with finite order not only fixes a point, but also maps a pencil of geodesics to itself. We apply similar techniques to the automorphism group of a smoothly bounded domain in the complex plane having connectivity three or more. We show that any prime dividing the order of this finite group must divide a certain integer depending only on the connectivity of the domain.

math.DG↗

arXiv2023

A Systolic Inequality for the Filling Area Conjecture

We prove an upper bound on the systolic ratio of an orientable isometric filling of the circle equipped with a Riemannian metric. The bound depends only on the genus of isometric filling. We also apply the bound to the class of orientable isometric filling with a certain lower bound on the systole. We deduce that the Filling Area Conjecture holds true for this class when the genus is sufficiently large.

math.DG↗

arXiv2023

Some Characterisations of p-adic Analytic Groups

We give three necessary and sufficient conditions for a pro-p group to be p-adic analytic. We show that a noetherian pro-p group having finite chain length has a finite rank and conversely. We further deduce that a noetherian pro-p group has a finite rank precisely when it satisfies the weak descending chain condition. Using these results, we resolve a conjecture posed by Lubotzky and Mann in the affirmative within the class of noetherian groups which are countably based. Using these results, we answer a related conjecture about pro-p groups for the case of countably based pro-p groups. Namely, we prove that if every closed but non-open subgroup of a countably based pro-p group has finite rank, then the group is p-adic analytic and conversely.

math.GR↗

arXiv2017

A Simple Generalised Plancherel Formula for Compactly Induced Characters

The aim of this article is to present a simple generalized Plancherel formula for a locally compact unimodular topological group G of type I. This formula specializes to the Whittaker-Plancherel formula for a split reductive p-adic group of Sakellaridis-Venkatesh and differs from that of a quasi-split p-adic group due to Delorme. Furthermore, it also applies to certain metaplectic groups and other interesting situations where the local theory of distinguished representations has been studied.

math.RT↗