paper

Simplicial volumes in Bruhat-Tits buildings of split classical type

arXiv:2210.03328

Abstract

In a Bruhat-Tits building of split classical type (that is, of type $A_{n}$ , $B_{n}$ , $C_{n}$ , $D_{n}$ , and any combination of them) over a local field, the simplicial volume counts the vertices within the given simplicial distance from a special vertex. This paper aims to study the asymptotic growth of the simplicial volume. A formula of the simplicial volume is deduced from the theory of concave functions. Then the dominant term in its asymptotic growth is found using the theory of $q$ -exponential polynomials developed in this paper.

150 pages