# Toward a minimal model for $H_\ast(\overline{\mathcal{M}})$.

@article{Ward2020TowardAM, title={Toward a minimal model for \$H\_\ast(\overline\{\mathcal\{M\}\})\$.}, author={Benjamin C. Ward}, journal={arXiv: Algebraic Topology}, year={2020} }

The modular operad $H_\ast(\overline{\mathcal{M}}_{g,n})$ 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 $H_\ast(\mathcal{M}_{g,n})$. Using Getzler's elliptic relation, we give an explicit construction of the first family of such higher operations.

## References

SHOWING 1-10 OF 20 REFERENCES

### Oriented hairy graphs and moduli spaces of curves

- Mathematics
- 2020

We discuss a graph complex formed by directed acyclic graphs with external legs. This complex comes in particular with a map to the ribbon graph complex computing the (compactly supported) cohomology…

### Modular Operads

- Mathematics
- 1994

We develop a \higher genus" analogue of operads, which we call modular operads, in which graphs replace trees in the deenition. We study a functor F on the category of modular operads, the Feynman…

### The second homology group of the mapping class group of an orientable surface

- Mathematics
- 1983

In I-7] Mumford shows that the Picard group P ic (~ ' ) is isomorphic to H2(F; 2~) and conjectures the latter is rank one, g>3 . We prove this below for g>5 . Another interpretation of this theorem…

### Intersection theory on M̄1,4 and elliptic Gromov-Witten invariants

- Mathematics
- 1997

We find a new relation among codimension 2 algebraic cycles in the moduli space M1,4, and use this to calculate the elliptic Gromov-Witten invariants of projective spaces CP and CP.…

### Deformation theory of Cohomological Field Theories

- Mathematics
- 2020

We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce…

### Feynman Categories

- Mathematics
- 2017

In this paper we give a new foundational categorical formulation for operations and relations and objects parameterizing them. This generalizes operads and all their cousins including but not limited…

### The structure of the tautological ring in genus one

- Mathematics
- 2014

We prove Getzler's claims about the cohomology of the moduli space of stable curves of genus one, that is, that the even cohomology ring is spanned by the strata classes and that all relations…

### The Semi-Classical Approximation for Modular Operads

- Mathematics
- 1996

Abstract:We study the contribution of one-loop graphs (the semi-classical expansion) problem in the setting of modular operads. As an application, we calculate the Betti numbers of the…

### Six operations formalism for generalized operads

- Mathematics
- 2017

This paper shows that generalizations of operads equipped with their respective bar/cobar dualities are related by a six operations formalism analogous to that of classical contexts in algebraic…

### Two-dimensional topological gravity and equivariant cohomology

- Mathematics
- 1994

The analogy between topological string theory and equivariant cohomology for differentiable actions of the circle group on manifolds has been widely remarked on. One of our aims in this paper is to…