On contact mapping classes of prequantizations

TL;DR

This paper demonstrates the existence of infinitely many smoothly trivial contact mapping classes in certain prequantizations, exploring their relation to symplectomorphisms and the lifting problem.

Contribution

It provides explicit examples of prequantizations with infinitely many contact mapping classes and analyzes the lifting problem of symplectomorphisms to contactomorphisms.

Findings

Existence of infinitely many smoothly trivial contact mapping classes.

Connection between contactomorphisms and symplectomorphisms.

Insights into the lifting problem of symplectomorphisms.

Abstract

We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which project to the identity component of the symplectomorphism group of the base manifold. Along the way, we study the lifting problem of symplectomorphisms of the base manifold to strict contactomorphisms of the prequantization.