The string topology coproduct on complex and quaternionic projective space

TL;DR

This paper computes the string topology coproduct on the free loop space of complex and quaternionic projective spaces using explicit cycles, revealing the behavior of the Goresky-Hingston product for these spaces.

Contribution

It introduces explicit cycles to compute the string topology coproduct on complex and quaternionic projective spaces, advancing understanding of their loop space homology.

Findings

Computed the string topology coproduct for these spaces

Determined the behavior of the Goresky-Hingston product

Provided explicit cycles generating homology

Abstract

On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these explicit cycles to compute the string topology coproduct on complex and quaternionic projective space. The behavior of the Goresky-Hingston product for these spaces then follows directly.