Rational curvature invariants for 2-complexes
Henry Wilton
TL;DR
This paper surveys new rational curvature invariants for 2-complexes, discussing their properties, examples, and conjectures, providing a foundation for understanding curvature bounds in combinatorial topology.
Contribution
It compiles and discusses theorems, examples, and conjectures related to newly defined rational curvature invariants for 2-complexes.
Findings
Invariants are rational and computable.
Theorems about curvature bounds are established.
Examples illustrate the invariants' applications.
Abstract
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems about these invariants, computes examples, and lays out a programme of conjectures.
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Taxonomy
TopicsGeometric and Algebraic Topology · Point processes and geometric inequalities · Topological and Geometric Data Analysis