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Title: Homotopy sheaves on manifolds and applications to spaces of smooth embeddings
Author: Boavida de Brito, Pedro
ISNI:       0000 0004 5348 8134
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 2014
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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.
Supervisor: Not available Sponsor: Fundãçao para a Ciência e a Tecnologia
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Homotopy theory ; Manifolds (Mathematics) ; Operads ; Harmonic analysis