Given a lagrangian link with k components in the disc, it is possible to define an associated Hofer norm on the braid group with k strands. In this talk we are going to detail this definition, and explain how it is possible to prove non degeneracy if k=2 and certain area conditions on the lagrangian link are met. The proof is based on the construction, using Quantitative Heegaard-Floer Homology, of a family of quasimorphisms which detect linking numbers of braids. Time permitting, we are also going to see how to extend the results to any compact surface with boundary. This talk is based on work of mine, and an ongoing project with Ibrahim Trifa (for the higher genus case).
Hofer Norms on Braid Groups and Quantitative Heegaard-Floer Homology
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Nom de l'orateur
Francesco Morabito
Etablissement de l'orateur
Ecole Polytechnique
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