# Small Nijenhuis tensors on compact almost complex manifolds with no complex structure

## Scott Wilson

created by daniele on 05 Jan 2021
modified on 29 Mar 2021

14 apr 2021 -- 15:30

Firenze (online)

Seminario di Geometria Differenziale e Analisi Complessa del Dipartimento di Matematica e Informatica "Ulisse Dini" dell'Università di Firenze

Abstract.

I will present several examples of compact almost complex manifolds with a $1$-parameter family of almost complex structures having arbitrarily small Nijenhuis tensors in the $C^0$-norm. The $4$-dimensional examples possess no complex structure, while the $6$-dimensional examples do not possess left invariant complex structures, and whether they possess complex structures appears to be unknown. This is joint work with Luis Fernandez and Tobias Shin.

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