Interval topology in contact geometry

TL;DR

This paper introduces a new topology on spaces of Legendrian submanifolds and contactomorphism groups, inspired by Lorentzian Alexandrov topology, to advance the understanding of contact geometry structures.

Contribution

It defines a novel topology in contact geometry, bridging concepts from Lorentzian geometry to study Legendrian submanifolds and contactomorphisms.

Findings

Topology on Legendrian submanifolds established

Topology on contactomorphism groups introduced

Motivated by Alexandrov topology in Lorentz geometry

Abstract

A topology is introduced on spaces of Legendrian submanifolds and groups of contactomorphisms. The definition is motivated by the Alexandrov topology in Lorentz geometry.