The three cusps conjecture

Abstract

We prove Arnol'd's three cusps conjecture about the front of Legendrian curves in the projectivized cotangent bundle of the $2$-sphere. We use the microlocal theory of sheaves of Kashiwara and Schapira and study the derived category of sheaves on the $2$-sphere with a given smooth Lagrangian microsupport.

References in corpus (1)

• Microlocal condition for non-displaceablility

Cited by in corpus (7)

• The conormal torus is a complete knot invariant
• Calabi-Yau structures on topological Fukaya categories
• Persistent homology and microlocal sheaf theory
• Radon Transform for Sheaves
• Projected distances for multi-parameter persistence modules
• Quantitative Tamarkin category
• Piecewise linear sheaves