Givental's non-linear Maslov index on lens spaces

Abstract

Givental's non-linear Maslov index, constructed in 1990, is a quasimorphism on the universal cover of the identity component of the contactomorphism group of real projective space. This invariant was used by several authors to prove contact rigidity phenomena such as orderability, unboundedness of the discriminant and oscillation metrics, and a contact geometric version of the Arnold conjecture. In this article we give an analogue for lens spaces of Givental's construction and its applications.

44 pages; v3: minor changes; v2: besides minor changes, we corrected a mistake in Corollary 1.3(iv)

References in corpus (1)

• Translated points for contactomorphisms of prequantization spaces over monotone symplectic toric manifolds

Cited by in corpus (4)

• Contactomorphism groups and Legendrian flexibility
• Translated points for contactomorphisms of prequantization spaces over monotone symplectic toric manifolds
• Generating functions in symplectic and contact geometry
• The cohomological index of free $\mathbb{Z}/p$-actions is not additive with respect to join