Date of Award
8-2016
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Ralph Kaufmann
Committee Chair
Ralph Kaufmann
Committee Member 1
James McClure
Committee Member 2
David B. McReynolds
Committee Member 3
Jeremy Miller
Abstract
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.
Recommended Citation
Lucas, Jason M., "Connecting models of configuration spaces: From double loops to strings" (2016). Open Access Dissertations. 802.
https://docs.lib.purdue.edu/open_access_dissertations/802