Cohomology of the continuous hull of a combinatorial pentagonal tiling

TL;DR

This paper computes the cohomology and topological K-theory of the continuous hull associated with a regular pentagonal tiling of the plane, building on previous constructions of the hull as an inverse limit.

Contribution

It introduces methods to calculate the cohomology and K-theory of the hull, advancing the understanding of its topological properties.

Findings

Computed the cohomology groups of the hull

Determined the topological K-theory of the hull

Connected the tiling's combinatorics with topological invariants

Abstract

In the article "Construction of the continuous hull for the combinatorics of a regular pentagonal tiling of the plane" we constructed the continuous hull for the combinatorics of "A regular pentagonal tiling of the plane", and in the article "Continuous hull of a combinatorial pentagonal tiling as an inverse limit" we showed how we could write this hull as an inverse limit. In this paper we show how to compute the cohomology of the hull and its topological K-theory.