Doctor of Philosophy
This thesis is concerned with the study of rationally smooth group embeddings. We prove that the equivariant cohomology of any of these compactifications
can be described, via GKM-theory, as certain ring of piecewise polynomial functions.
Moreover, building on previous work of Renner, we show that the embeddings under consideration come equipped with both a canonical decomposition into rational cells and a filtration by equivariantly formal closed subvarieties.
The techniques developed in this monograph supply a method for constructing free
module generators on the equivariant cohomology of Q-filtrable GKM-varieties.
Our findings extend the earlier work of Arabia and Guillemin-Kogan on equivariant characteristic classes.
In the last two chapters of this work, inspired by the papers of Brion and Renner,
we compute explicitly the GKM characters associated to any group embedding.
Our major result describes the equivariant cohomology of rationally smooth embeddings in terms of roots, idempotents, and underlying monoid data.
Gonzales, Richard P., "GKM theory of rationally smooth group embeddings" (2011). Electronic Thesis and Dissertation Repository. 216.