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The quotient cohomology of tiling spaces is a topological invariant thatrelates a tiling space to one of its factors, viewed as topological dynamicalsystems. In particular, it is a relative version of the tiling cohomology thatdistinguishes factors of tiling spaces. In this work, the quotient cohomologieswithin certain families of substitution tiling spaces in 1 and 2 dimensions aredetermined. Specifically, the quotient cohomologies for the family of thegeneralised Thue-Morse sequences and generalised chair tilings are presented.

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