Work

Equivariant covering type and the number of vertices in equivariant triangulations

Year: 2024

Type: article

Abstract: We introduce the notion of the equivariant covering type of a space X on which a finite group G acts and study its properties. The equivariant covering type measures the size of G-equivariant good covers of X and is thus an extension of the covering type of a space, introduced by Karoubi and Weibel. We show that the equivariant covering type is a G-homotopy invariant and describe its relation with other G-invariants, like the equivariant LS-category, G-genus, and the multiplicative structures of equivariant cohomology theories. We also compute the G-covering type of regular G-graphs, give estimates for orientation-preserving actions on surfaces and for the projectivizations of complex representations of G and cohomology spheres. As an application, we derive estimates of sizes of minimal G-triangulations for various G-spaces.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2024.110

Authors: Dejan Govc, Wacław Marzantowicz, Petar Pavešić

Institutions: University of Ljubljana, Institute of Mathematics, Physics, and Mechanics, Adam Mickiewicz University in Poznań

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Javna Agencija za Raziskovalno Dejavnost RS

Awards: Selected problems in applied and computational topology, Topology and its applications