An elementary proof of the string topology structure of compact oriented surfaces

TL;DR

This paper provides a new, elementary algebraic topology proof of the string topology structure on compact oriented surfaces of genus at least 2, reaffirming Vaintrob's earlier results.

Contribution

It offers a simplified, elementary proof of the string topology structure for surfaces, avoiding complex techniques used previously.

Findings

Confirmed the string topology structure for genus ≥ 2 surfaces

Provided an elementary alternative proof to Vaintrob's result

Simplified understanding of surface string topology

Abstract

We give a new proof of the string topology structure of a compact oriented surface of genus g greater than or equal to 2, using elementary algebraic topology. This reproves the result of Vaintrob.