Holonomy and the Newlander-Nirenberg theorem in $b^k$-geometry

Abstract: Melrose introduced $b$-geometry as a paradigm for studying operators on a manifold that suffer a first-order degeneracy along a hypersurface. Scott considered higher-order degeneracies, introducing $b^k$-geometry for $k>1$. In this talk we consider two different aspects of (a slight variation of) Scott's $b^k$-geometry: one global and one local. Firstly, we discuss the classification of $b^k$-geometries by a holonomy invariant (similar results were obtained independently by Bischoff-del Pino-Witte). We also discuss the Newlander-Nirenberg for complex $b^k$-manifolds. Complex $b$-manifolds ($k=1$) were defined by Mendoza the Newlander-Nirenberg theorem for $b$-manifolds was obtained by Francis-Barron.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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