Operations on stable moduli spaces

TL;DR

This paper develops new operations on stable moduli spaces to compare their cohomology, establishing isomorphisms under specific conditions related to Euler characteristics and prime valuations.

Contribution

It introduces operations on stable moduli spaces and provides criteria for cohomology isomorphisms based on Euler characteristics and prime valuations.

Findings

Established isomorphisms in cohomology under stable conditions

Connected Euler characteristic valuations with cohomological equivalences

Provided tools for comparing moduli spaces of manifolds with tangential structures

Abstract

We construct certain operations on stable moduli spaces and use them to compare cohomology of moduli spaces of closed manifolds with tangential structure. We obtain isomorphisms in a stable range provided the $p$-adic valuation of the Euler characteristics agree, for all primes $p$ not invertible in the coefficients for cohomology.