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Cohomology in algebra, geometry, physicsand statistics
On Legendrian products and twist spuns
Speaker’s name:
Roman Golovko
Speaker’s affiliation:
Charles University
Place:
in IM building, ground floor
Date:
Wednesday, 26. June 2019 - 11:30 to 12:30
Abstract:
The Legendrian product of two Legendrian knots, as defined by Lambert-Cole,
is a Legendrian torus. We show that this Legendrian torus is a twist spun whenever one of
the Legendrian knot components is sufficiently large. We then study examples of Legendrian
products which are not Legendrian isotopic to twist spuns. In order to do this, we prove a
few structural results on the bilinearised Legendrian contact homology and augmentation
variety of a twist spun. Finally, using the properties of the augmentation variety of a
twist spun, we show that the Legendrian lifts of the Clifford torus and
Chekanov torus are not twist spuns, and argue why the Legendrian lifts of infinite family of
Vianna's monotone Lagrangian tori in CP2 are not twist spuns.
is a Legendrian torus. We show that this Legendrian torus is a twist spun whenever one of
the Legendrian knot components is sufficiently large. We then study examples of Legendrian
products which are not Legendrian isotopic to twist spuns. In order to do this, we prove a
few structural results on the bilinearised Legendrian contact homology and augmentation
variety of a twist spun. Finally, using the properties of the augmentation variety of a
twist spun, we show that the Legendrian lifts of the Clifford torus and
Chekanov torus are not twist spuns, and argue why the Legendrian lifts of infinite family of
Vianna's monotone Lagrangian tori in CP2 are not twist spuns.