Behavior of the Eilenberg-Moore spectral sequence in derived string topology

TL;DR

This paper explores the behavior of the Eilenberg-Moore spectral sequence in derived string topology, focusing on its applications to Gorenstein spaces and functorial properties in Poincaré duality spaces.

Contribution

It provides new applications of the Eilenberg-Moore spectral sequence to relative loop homology and establishes its functoriality in specific topological categories.

Findings

Spectral sequence converges to the relative loop homology algebra.

Demonstrates functoriality on simply-connected Poincaré duality spaces.

Provides applications to Gorenstein spaces in derived string topology.

Abstract

The purpose of this paper is to give applications of the Eilenberg-Moore type spectral sequence converging to the relative loop homology algebra of a Gorenstein space, which is introduced in the previous paper due to the authors. Moreover, it is proved that the spectral sequence is functorial on the category of simply-connected Poincar\'e duality spaces over a space.