Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Dr. Keri Sather-Wagstaff

Committee Member

Dr. Michael Burr

Committee Member

Dr. James Coykendall

Committee Member

Dr. Felice Manganiello


We investigate algebra structures on resolutions of a special class of Cohen-Macaulay simplicial complexes. Given a simplicial complex, we define a pure simplicial complex called the purification. These complexes arise as a generalization of certain independence complexes and the resultant Stanley-Reisner rings have numerous desirable properties, e.g., they are Cohen-Macaulay. By realizing the purification in the context of work of D'alì, et al., we obtain a multi-graded, minimal free resolution of the Alexander dual ideal of the Stanley-Reisner ideal. We augment this in a standard way to obtain a resolution of the quotient ring, which is likewise minimal and multi-graded. Ultimately, we propose an explicit product on the resolution and prove that, if associative, this product imparts a differential graded (DG) algebra structure on the minimal resolution.



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