The Teichmüller Stack

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

Abstract

This paper is a comprehensive introduction to the results of Meersseman (The Teichmüller and Riemann Moduli Stacks, Available via arxiv. http://arxiv.org/abs/1311.4170, 2015). It grew as an expanded version of a talk given at INdAM Meeting Complex and Symplectic Geometry, held at Cortona in June 12–18, 2016. It deals with the construction of the Teichmüller space of a smooth compact manifold M (that is the space of isomorphism classes of complex structures on M) in arbitrary dimension. The main problem is that, whenever we leave the world of surfaces, the Teichmüller space is no more a complex manifold or an analytic space but an analytic Artin stack. We explain how to construct explicitly an atlas for this stack using ideas coming from foliation theory. Throughout the article, we use the case of \(\mathbb{S}^{3} \times \mathbb{S}^{1}\) as a recurrent example.

Notes

Acknowledgements

Many thanks to Daniele Angella, Paolo de Bartolomeis, Costantino Medori and Adriano Tomassini for organizing this beautiful conference in Cortona.

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Copyright information

© Springer International Publishing AG, a part of Springer Nature 2017

Authors and Affiliations

  1. 1.LAREMA, UMR 6093 CNRSFaculté des SciencesAngers cedex 01France

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