The space of paths in complex projective space with real boundary conditions

TL;DR

This paper computes the integral homology and algebraic structure of the space of paths in complex projective space with real boundary conditions, revealing new topological insights.

Contribution

It provides the first detailed calculation of the homology and algebra structure of these path spaces with real boundary conditions in complex projective space.

Findings

Computed the integral homology of the path space

Determined the algebra structure with Pontryagin-Chas-Sullivan product

Established results with $\

Abstract

We compute the integral homology of the space of paths in $\mathbb{C}P^n$ with endpoints in $\mathbb{R}P^n$, $n \ge 1$ and its algebra structure with respect to the Pontryagin-Chas-Sullivan product with $\mathbb{Z}/2$-coefficients.