相关论文: Oriented hairy graphs and moduli spaces of curves

We give a detailed explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture for the special case of symplectic manifolds. We will show how the weights for the…

We compute the cohomology ring of a generalised type of configuration space of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and…

Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath…

In this work we study the homotopy type of multipath complexes of bidirectional path graphs and polygons, motivated by works of Vre\'cica and \v{Z}ivaljevi\'c on cycle-free chessboard complexes (that is, multipath complexes of complete…

We compactify the classical moduli variety of compact Riemann surfaces by attaching moduli of (metrized) graphs as boundary. The compactifications do not admit the structure of varieties and patch together to form a big connected moduli…

We continue the analysis of the geometry of generic Minkowski $\mathcal{N} = 1$, $D = 4$ flux compactifications in M-theory using exceptional generalised geometry, including the calculation of the infinitesimal moduli spaces. The…

If $R$ is a commutative ring, $M$ a compact $R$-oriented manifold and $G$ a finite graph without loops or multiple edges, we consider the graph configuration space $M^G$ and a Bendersky-Gitler type spectral sequence converging to the…

These notes loosely follow an introductory course on graph complexes, held at Humboldt-Universit\"at zu Berlin in summer 23. Instead of simply typing up my lecture notes I decided to give here an overview over (parts of) the topic (lecture…

This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a…

This paper extends results of Hatcher and Vogtmann's work "Cerf Theory for Graphs" to ribbon graphs. Given an orientable, punctured and basepointed surface Sigma, we prove that the space of ribbon graphs that can be drawn in Sigma is…

We introduce real-valued $(p,q)$-forms on weighted metric graphs with boundary similar to Lagerberg forms on polyhedral spaces. We compute the Dolbeault cohomology and prove Poincar\'e duality. Using Thuillier's thesis, the skeleton of a…

In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs, and focus on their (twisted) cohomology groups. We…

We study the topology of the link $M^{\mathrm{trop}}_{g,n}[1]$ of the tropical moduli spaces of curves when g=2. Tropical moduli spaces can be identified with boundary complexes for $\mathcal{M}_{g,n}$, as shown by…

The paper is devoted to the study of the orientability of the moduli spaces of real pseudoholomorphic curves in real symplectic manifolds. We begin by extending the results we obtained in \cite{article1}. Namely, we consider a complex…

We use orientations on stable graphs to express the combinatorial structure of the compactified universal Jacobians in degrees g-1 and g over the moduli space of stable curves, \Mgb, and construct for them graded stratifications compatible…

Building on previous work by Cameron et al. in [3], we give a recurrence for computing the number of acyclic orientations of complete $k$-partite graphs, which can be implemented to obtain a dynamic programming algorithm running in time…

The moduli space of rank $n$ graphs, the outer automorphism group of the free group of rank $n$ and Kontsevich's Lie graph complex have the same rational cohomology. We show that the associated Euler characteristic grows like…

We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose…

This is preprint HAL-00429963 (2009). I describe a combinatorial construction of the cohomology classes in compactified moduli spaces of curves $\widehat{Z}_{I}\in H^{*}(\bar{\mathcal{M}}_{g,n})$ starting from the following data: an odd…

The enumerative geometry of r-th roots of line bundles is the subject of Witten's conjecture and occurs in the calculation of Gromov-Witten invariants of orbifolds. It requires the definition of the suitable compact moduli stack and the…