arXiv subjects

Enrico Paolo Bugarin

Publications and source records attributed to Enrico Paolo Bugarin.

2 recordsLinked to original sources

arXiv2014

Quotient cohomology of certain 1- and 2-dimensional substitution tiling spaces

The quotient cohomology of tiling spaces is a topological invariant that relates a tiling space to one of its factors, viewed as topological dynamical systems. In particular, it is a relative version of the tiling cohomology that distinguishes factors of tiling spaces. In this work, the quotient cohomologies within certain families of substitution tiling spaces in 1 and 2 dimensions are determined. Specifically, the quotient cohomologies for the family of the generalised Thue-Morse sequences and generalised chair tilings are presented.

math.AT↗

arXiv2012

On Bravais colourings of cyclotomic integers with class number one

Given a Bravais colouring of planar modules $\M_n:=\Z[ξ_n]$, where $ξ_n$ is a primitive $n$th root of unity, two important colour groups arise: the colour symmetry group $H$, which permutes the colours of a given colouring of $\M_n$, and the colour preserving group $K$, a normal subgroup of $H$ that fixes the colours. This paper gives a complete characterisation of $H$ and $K$ for all $\ell$-colourings of $\M_n$ for values of $n$ for which $\M_n$ has class number one.

math.RA↗