Geometry of Maslov cycles

TL;DR

This paper introduces the concept of induced Maslov cycle, unifying various geometric and topological invariants across diverse mathematical fields such as algebraic and sub-Riemannian geometry.

Contribution

It presents a new framework for understanding invariants through the induced Maslov cycle, linking different areas of geometry and topology.

Findings

Defines the induced Maslov cycle and its properties.

Unifies invariants in algebraic and sub-Riemannian geometry.

Provides a new perspective on geometric and topological problems.

Abstract

We introduce the notion of induced Maslov cycle, which describes and unifies geometrical and topological invariants of many apparently unrelated problems, from Real Algebraic Geometry to sub-Riemannian Geometry.