Please use this identifier to cite or link to this item: http://hdl.handle.net/2307/5999
Title: From String structures to Spin structures on loop spaces
Authors: Capotosti, Alessandra
metadata.dc.contributor.advisor: Fiorenza, Domenico
Keywords: String
Loop
Spin
Structures
Stacks
Issue Date: 27-Apr-2016
Publisher: Università degli studi Roma Tre
Abstract: Let X be a n-dimensional smooth manifold, with n 3. In a series of papers culminating in Spin structures on loop spaces that characterize string manifolds, arXiv:1209.1731, Konrad Waldorf recently gave the first rigorous proof that a String structure on X induces a Spin structure on its loop space. Here we give a closely related but independent proof of this result by working in the more general setting of smooth stacks. In particular, the crucial point in our proof is the existence of a natural morphism of smooth stacks BSpin ! B2(BU(1)conn) refining the first fractional Pontryagin class. Once this morphism is exhibited, we show how Waldorf’s result follows from general constructions in the setting of smooth stacks.
URI: http://hdl.handle.net/2307/5999
Access Rights: info:eu-repo/semantics/openAccess
Appears in Collections:T - Tesi di dottorato
Dipartimento di Matematica e Fisica

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