Global homotopies for differential Hochschild cohomologies

Abstract: It is well known that the Hochschild–Kostant–Rosenberg map from multivector fields to differential Hochschild cochains is a quasi-isomorphism. Nevertheless, it is sometimes desirable to not only know the cohomology itself, but also find reasonable formulas for primitives of exact cochains. In my talk I will explain how to construct a quasi-inverse of the Hochschild–Kostant–Rosenberg map and a homotopy to turn all the maps into a deformation retract. The difference to already existing attempts is that our construction is performed globally and enjoys nice properties regarding symmetries. Moreover, the idea of this construction allows for generalizations in various directions. This is a joint work with Marvin Dippell, Chiara Esposito and Stefan Waldmann.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: https://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09

Meeting ID: 918 7552 8987 Password: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.

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