String topology on Gorenstein spaces

TL;DR

This paper introduces a unified framework for defining string operations on Gorenstein spaces, extending classical concepts to a broader class of spaces including classifying spaces and homotopy quotients, with implications for homotopy invariance and explicit calculations.

Contribution

It provides a simple, general setting for string operations on Gorenstein spaces, demonstrating homotopy invariance and enabling explicit computations.

Findings

Established a general framework for string operations on Gorenstein spaces.

Proved homotopy invariance of the string operations.

Enabled explicit calculations of string operations on various spaces.

Abstract

The purpose of this paper is to describe a general and simple setting for defining $(g,p+q)$-string operations on a Poincar\'e duality space and more generally on a Gorenstein space. Gorenstein spaces include Poincar\'e duality spaces as well as classifying spaces or homotopy quotients of connected Lie groups. Our presentation implies directly the homotopy invariance of each $(g,p+q)$-string operation as well as it leads to explicit computations.