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Cohomologies on Hypercomplex Manifolds

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Complex and Symplectic Geometry

Part of the book series: Springer INdAM Series ((SINDAMS,volume 21))

Abstract

We review some cohomological aspects of complex and hypercomplex manifolds and underline the differences between both realms. Furthermore, we try to highlight the similarities between compact complex surfaces on one hand and compact hypercomplex manifolds of real dimension 8 with holonomy of the Obata connection in \(\mathrm{SL}(2, \mathbb{H})\) on the other hand.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Bronx Community College of CUNY, Bronx, NY, 10453, USA

    Mehdi Lejmi

  2. Département de Mathématiques, Université libre de Bruxelles, CP218, Brussels, 1050, Belgium

    Patrick Weber

Authors
  1. Mehdi Lejmi
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  2. Patrick Weber
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Correspondence to Mehdi Lejmi .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Informatica ‘Ulisse Dini’, University of Florence, Firenze, Italy

    Daniele Angella

  2. Dipartimento di Scienze Matematiche, Fisiche e Informatiche, University of Parma, Parma, Italy

    Costantino Medori

  3. Dipartimento di Scienze Matematiche, Fisiche e Informatiche, University of Parma, Parma, Italy

    Adriano Tomassini

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Lejmi, M., Weber, P. (2017). Cohomologies on Hypercomplex Manifolds. In: Angella, D., Medori, C., Tomassini, A. (eds) Complex and Symplectic Geometry. Springer INdAM Series, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-319-62914-8_9

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