On ring-valued invariants of topological pairs

TL;DR

This paper introduces a new approach to defining ring-valued invariants of topological pairs using the concept of Δ-groupoids, providing an intrinsic topological framework for these invariants.

Contribution

It presents a novel method for constructing ring-valued invariants of topological pairs based on Δ-groupoids, advancing the algebraic tools available in topology.

Findings

Ring-valued invariants are defined intrinsically for topological pairs.

The approach utilizes Δ-groupoids to capture topological information.

Provides a new algebraic perspective on topological invariants.

Abstract

Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.