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Homotopy equivalence of nearby Lagrangians and the Serre spectral sequence
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.ORCID iD: 0000-0003-2618-5712
2017 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 368, no 3-4, p. 945-970Article in journal (Refereed) Published
Abstract [en]

We construct using relatively basic techniques a spectral sequence for exact Lagrangians in cotangent bundles similar to the one constructed by Fukaya, Seidel, and Smith. That spectral sequence was used to prove that exact relative spin Lagrangians in simply connected cotangent bundles with vanishing Maslov class are homology equivalent to the base (a similar result was also obtained by Nadler). The ideas in that paper were extended by Abouzaid who proved that vanishing Maslov class alone implies homotopy equivalence. In this paper we present a short proof of the fact that any exact Lagrangian with vanishing Maslov class is homology equivalent to the base and that the induced map on fundamental groups is an isomorphism. When the fundamental group of the base is pro-finite this implies homotopy equivalence.

Place, publisher, year, edition, pages
2017. Vol. 368, no 3-4, p. 945-970
National Category
Geometry Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-332931DOI: 10.1007/s00208-016-1447-5ISI: 000406037300004OAI: oai:DiVA.org:uu-332931DiVA, id: diva2:1157443
Available from: 2017-11-16 Created: 2017-11-16 Last updated: 2017-11-16Bibliographically approved

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