Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Ralph Kaufmann

Committee Chair

Ralph Kaufmann

Committee Member 1

James McClure

Committee Member 2

David B. McReynolds

Committee Member 3

Jeremy Miller


Foundational to the subject of operad theory is the notion of an En operad, that is, an operad that is quasi-isomorphic to the operad of little n-cubes Cn. They are central to the study of iterated loop spaces, and the specific case of n = 2 is key in the solution of the Deligne Conjecture. In this paper we examine the connection between two E 2 operads, namely the little 2-cubes operad C 2 itself and the operad of spineless cacti. To this end, we construct a new suboperad of C2, which we name the operad of tethered 2-cubes. Much of our analysis involves examining trees labeled by elements of the operad of little intervals, C1. In the final chapter, we generalize this idea of graphs decorated by elements of an operad to the notion of a decorated Feynman category, building off of the work of Kaufmann and Ward. As an immediate application, we will give a simple definition of non-Σ modular operads.

Included in

Mathematics Commons