Beyond the Elliptic Genus

TL;DR

This paper introduces a new cobordism invariant for Riemannian manifolds, extending the concept of the elliptic genus and sharing similar properties, applicable under specific restrictions on the manifold and surface.

Contribution

It generalizes the elliptic genus to a broader class of manifolds, providing a new invariant with comparable properties.

Findings

Constructed a new cobordism invariant for Riemannian manifolds.

Extended the elliptic genus to a more general setting.

Demonstrated properties similar to the elliptic genus.

Abstract

Given a Riemann surface and a riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties.