
Poincaré duality for families of supermanifolds
The seminar series covers topics in Algebra and Topology
Date & time
Date/time
18 Mar 2025 3:00pm - 18 Mar 2025 4:00pm
Speaker
Speakers
John Huerta
Event series
Event series
Contact
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Description
Abstract:
It is well known to experts, but seldom discussed explicitly, that smooth supergeometry is best done in families. This is also called the relative setting, and it implies that we need relative versions of standard supergeometric constructions. Such constructions include the de Rham complex familiar from ordinary differential geometry, but in the supergeometric setting, they also include more exotic objects, such as the Berezinian line bundle (whose sections are the correct objects to integrate over supermanifolds) and the related complex of integral forms, where the super version of Stokes' theorem lives. To work in families, we introduce relative versions of the de Rham complex and the integral form complex, and we prove that they satisfy a relative version of Poincaré duality. No background in supergeometry will be assumed for this talk.
This is joint work with Konstantin Eder and Simone Noja.
Location
Rm 1.33, Hanna Neumann Building #145
-35.275389387895, 149.11926090717