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Forum Mathematicum

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Volume 28, Issue 5


Symplectic Lefschetz fibrations on adjoint orbits

Elizabeth Gasparim / Lino Grama
  • Imecc – Unicamp, Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz. 13083-859 Campinas - SP, Brazil
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/ Luiz A. B. San Martin
  • Imecc – Unicamp, Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz. 13083-859 Campinas - SP, Brazil
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Published Online: 2015-11-28 | DOI: https://doi.org/10.1515/forum-2015-0039


We prove that adjoint orbits of semisimple Lie algebras have the structure of symplectic Lefschetz fibrations. We describe the topology of the regular and singular fibres, in particular we calculate their middle Betti numbers.

Keywords: Lefschetz fibrations; Morse-type singularities; symplectic manifolds

MSC 2010: 32S50; 32L05; 53D99


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About the article

Received: 2015-02-25

Published Online: 2015-11-28

Published in Print: 2016-09-01

Funding Source: Fundação de Amparo à Pesquisa do Estado de São Paulo

Award identifier / Grant number: 2012/10179-5

Award identifier / Grant number: 2014/17337-0

Award identifier / Grant number: 2012/18780-0

Funding Source: Conselho Nacional de Desenvolvimento Científico e Tecnológico

Award identifier / Grant number: 303755/2009-1

The authors acknowledge support of Fapesp grants 2012/10179-5, 2014/17337-0, 2012/18780-0 and CNPq grant 303755/2009-1.

Citation Information: Forum Mathematicum, Volume 28, Issue 5, Pages 967–979, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0039.

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