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Cohomologies on almost complex manifolds and their applications 

October 2, 2019 @ 4:30 pm - 5:30 pm

10/2/2019 Colloquium
Speaker: Spiro Karigiannis (University of Waterloo)
Title: Cohomologies on almost complex manifolds and their applications

Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

 

\10/2/2019 Colloquium

Details

Date:
October 2, 2019
Time:
4:30 pm - 5:30 pm
Event Category:

Venue

CMSA
20 Garden Street
Cambridge, MA 02138 United States
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