Work

A note on $p$-adic simplicial volumes

Year: 2020

Type: article

Abstract: We define and study generalizations of simplicial volume over arbitrary seminormed rings with a focus on $p$-adic simplicial volumes. We investigate the dependence on the prime and establish homology bounds in terms of $p$-adic simplicial volumes. As the main examples we compute the weightless and $p$-adic simplicial volumes of surfaces. This gives a way to calculate classical simplicial volume of surfaces without hyperbolic straightening and shows that surfaces satisfy mod $p$ and $p$-adic approximation of simplicial volume.

Source: University of Regensburg Publication Server (University of Regensburg)

DOI: 10.48550/arxiv.2003.10756

Authors: Kionke, Steffen, Loeh, Clara

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3013545092

FWCI: 0.653

Cites: 20

Cited by: 2

Related to: 20