This thesis explores connections between homotopy sheaves, manifold calculus of functors and operad theory. We argue that there is a deep overlap between these, and as evidence we give a new operadic description of the homotopy theoretical obstructions to deforming a smooth immersion into a smooth embedding. We then discuss an application which improves on some aspects of recent results of Arone-Turchin and Dwyer-Hess concerning spaces of long knots and high-dimensional variants. Along the way, we define fibrewise complete Segal spaces, a mild generalisation of Rezk's notion of complete Segal spaces. Also in the context of Segal spaces, we define right fibrations and prove a Grothendieck construction theorem for presheaves with values in spaces. Finally, we prove a result of independent interest which states that weakly k-reduced operads (those with contractible space of operations in arity j ? k) can be strictified when k = 0, 1.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:629411 |
| Date | January 2014 |
| Creators | Boavida de Brito, Pedro |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=215123 |
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