Simplicial volumes in Bruhat-Tits buildings of split classical type

Xu Gao

Simplicial volumes in Bruhat-Tits buildings of split classical type

Number Theory 2022-10-10 v1 Algebraic Geometry Group Theory

Authors: Xu Gao

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.

Keywords

bruhat-tits buildings split classical type simplicial volume asymptotic growth concave functions q-exponential polynomials

Cite

@article{arxiv.2210.03328,
  title  = {Simplicial volumes in Bruhat-Tits buildings of split classical type},
  author = {Xu Gao},
  journal= {arXiv preprint arXiv:2210.03328},
  year   = {2022}
}

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150 pages

Simplicial volumes in Bruhat-Tits buildings of split classical type

Abstract

Keywords

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