Toward a minimal model for \(H_*(\overline{\mathcal {M}})\)

Abstract

The modular operad \(H_*(\overline{\mathcal {M}}_{g,n})\) of the homology of Deligne-Mumford compactifications of moduli spaces of pointed Riemann surfaces has a minimal model governed by higher homology operations on the open moduli spaces \(H_*(\mathcal {M}_{g,n})\). Using Getzler’s computation of relations among boundary cycles in \(H_4(\overline{\mathcal {M}}_{1,4})\), we give an explicit construction of the first family of such higher operations.