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Pattern-equivariant Cohomology of Tiling Spaces With Rotations. Edition No. 1
VDM Publishing House, July 2009, Pages: 68
Pattern-equivariant cohomology theory was developed
by Ian Putnam and Johannes Kellendonk in 2003, for
tilings whose tiles appear in fixed orientations. In
this dissertation, we generalize this theory in two
ways: first, we define this cohomology to apply to
tiling spaces, rather than individual tilings.
Second, we allow tilings with tiles appearing in
multiple orientations - possibly infinitely many.
Along the way, we prove an approximation theorem,
which has use beyond pattern-equivariant cohomology.
This theorem states that a function which is a
topological conjugacy can be approximated arbitrarily
a function which preserves the local structure of a
tiling space. The approximation theorem is limited to
translationally finite tilings, and we conjecture
that it is not true in the infinite case.
Betseygail Rand was born in Gainesville, Florida, on February
3rd, 1978, to proud parents Kenneth and Colleen Rand. Shortly
thereafter, she became an Assistant Professor at Texas Lutheran
University. She is married to Jamaal Fraser, and has one lovely
daughter, so far. Her parents are still proud of her.