Loops in surfaces and star-fillings

2019/10/03 by Turaev, Vladimir
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1910.01602

Abstract

We discuss a new approach to computing the standard algebraic operations on homotopy classes of loops in surfaces: the homological intersection number, Goldman's Lie bracket, and the author's Lie cobracket. Our approach uses fillings of the surfaces by certain graphs.

Related

• Separability criteria for loops via the Goldman bracket
• Minimal intersection of curves on surfaces
• Geometric intersections of loops on surfaces
• Lie algebras of curves and loop-bundles on surfaces
• Quasi-Lie bialgebras of loops in quasi-surfaces