On local integration of Lie brackets

Alejandro Cabrera
  • Corresponding author
  • Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro, RJ 21941-909, Brazil
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, Ioan Mărcuţ
  • IMAPP, Department of Mathematics, Radboud University Nijmegen, Heyendaalseweg 135, Nijmegen, 6500 GL, The Netherlands
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and María Amelia Salazar
  • Instituto de Matemática e Estatística, GMA, Universidade Federal Fluminense, Rua Professor Marcos Waldemar de Freitas Reis s/n, Gragoatá, Niterói, CEP: 24.210-201, Rio de Janeiro, Brazil
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Abstract

We give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field lifting the underlying anchor map. This construction leads to a complete account of local Lie theory and, in particular, to a finite-dimensional proof of the fact that the category of germs of local Lie groupoids is equivalent to that of Lie algebroids.

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