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b-Lab Diary of a confinement: Daniel Peralta (II)

In these days of confinement, work in the lab has not stopped! We are having talks by videoconference, both by members of the lab and by guests.

If a talk interests you and you wish to listen to attend, or if you have a proposal for these talks, please contact the organizer: .

Contact structures and Beltrami fields on the torus and the sphere

(This is the second part of this talk)

Speaker: Daniel Peralta-Salas

When: Tuesday 5th of May, at 17:00 - 18:00.

Abstract: We present new explicit tight and overtwisted contact structures on the (round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly compatible. Our proofs are based on the construction of nonvanishing curl eigenfields using suitable families of Jacobi or trigonometric polynomials. As a consequence, we show that the contact sphere theorem of Etnyre, Komendarczyk and Massot (2012) does not hold for weakly compatible metric as it was conjectured. We also establish a geometric rigidity for tight contact structures by showing that any contact form on the 3-sphere admitting a compatible metric that is the round one is isometric, up to a constant factor, to the standard (tight) contact form.

The talk will be tightly related to this article: https://arxiv.org/abs/2004.10185.