Multifraction reduction II: Conjectures for Artin–Tits groups

Multifraction reduction I: The 3-Ore case and Artin-Tits groups of type FC

We describe a new approach to the word problem for Artin-Tits groups and, more generally, for the enveloping group U(M) of a monoid M in which any two elements admit a greatest common divisor. The method relies on a rewrite system RM that extends free reduction for free groups. Here we show that, if M satisfies what we call the 3-Ore condition about common multiples, what corresponds to type FC...

Beilinson’s conjectures II

Exponential Sums, Ree Groups and Suzuki Groups: Conjectures

ISSN: 1058-6458 (Print) 1944-950X (Online) Journal homepage: http://www.tandfonline.com/loi/uexm20 Exponential Sums, Ree Groups and Suzuki Groups: Conjectures Nicholas M. Katz To cite this article: Nicholas M. Katz (2017): Exponential Sums, Ree Groups and Suzuki Groups: Conjectures, Experimental Mathematics, DOI: 10.1080/10586458.2017.1334246 To link to this article: http://dx.doi.org/10.1080/1...

Abelianization Conjectures for Some Arithmetic Square Complex Groups

We extend a conjecture of Kimberley-Robertson on the abelian-izations of certain square complex groups.

Novikov Conjectures for Arithmetic Groups with Large Actions at Infinity

We construct a new compactification of a noncompact rank one globally symmetric space. The result is a nonmetrizable space which also compactifies the Borel–Serre enlargement X of X , contractible only in the appropriate Čech sense, and with the action of any arithmetic subgroup of the isometry group of X on X not being small at infinity. Nevertheless, we show that such a compactification can b...