Work

Dimension and partial groups

Year: 2025

Type: article

Abstract: A partial group with n + 1 n+1 elements is, when regarded as a symmetric simplicial set, of dimension at most n n . This dimension is n n if and only if the partial group is a group. As a consequence of the first statement, finite partial groups are genuinely finite, despite being seemingly specified by infinitely much data. In particular, finite partial groups have only finitely many im-partial subgroups. We also consider dimension of partial groupoids.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17423

Authors: Philip Hackney, Rémi Molinier

Institutions: University of Louisiana at Lafayette, Institut Fourier, Université Grenoble Alpes

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, Louisiana Board of Regents, Université Grenoble Alpes, Agence Nationale de la Recherche