Tropical curves, graph complexes, and top weight cohomology of ℳ_ {ℊ}
We study the topology of a space $\Delta _ {g} $ parametrizing stable tropical curves of
genus $ g $ with volume $1 $, showing that its reduced rational homology is canonically …
genus $ g $ with volume $1 $, showing that its reduced rational homology is canonically …
The rational homotopy of mapping spaces of E operads
B Fresse, V Turchin, T Willwacher - arXiv preprint arXiv:1703.06123, 2017 - arxiv.org
We express the rational homotopy type of the mapping spaces $\mathrm {Map}^ h (\mathsf
D_m,\mathsf D_n^{\mathbb Q}) $ of the little discs operads in terms of graph complexes …
D_m,\mathsf D_n^{\mathbb Q}) $ of the little discs operads in terms of graph complexes …
Weight 11 compactly supported cohomology of moduli spaces of curves
S Payne, T Willwacher - International Mathematics Research …, 2024 - academic.oup.com
We study the weight 11 part of the compactly supported cohomology of the moduli space of
curves, using graph complex techniques, with particular attention to the case. As …
curves, using graph complex techniques, with particular attention to the case. As …
Invariant differential forms on complexes of graphs and Feynman integrals
F Brown - SIGMA. Symmetry, Integrability and Geometry: Methods …, 2021 - emis.de
We study differential forms on an algebraic compactification of a moduli space of metric
graphs. Canonical examples of such forms are obtained by pulling back invariant …
graphs. Canonical examples of such forms are obtained by pulling back invariant …
[PDF][PDF] Graph homology computations
S Brun, T Willwacher - arXiv preprint arXiv:2307.12668, 2023 - arxiv.org
arXiv:2307.12668v1 [math.QA] 24 Jul 2023 Page 1 arXiv:2307.12668v1 [math.QA] 24 Jul 2023
GRAPH HOMOLOGY COMPUTATIONS SIMON BRUN AND THOMAS WILLWACHER Abstract …
GRAPH HOMOLOGY COMPUTATIONS SIMON BRUN AND THOMAS WILLWACHER Abstract …
Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group
We compute the weight 2 (resp.~ top $-2$) cohomology of the Feynman transforms of the
cyclic (co) operads $\mathsf {BV} $, $ D\mathsf {BV} $, $\mathsf {Grav} $ and $\mathsf …
cyclic (co) operads $\mathsf {BV} $, $ D\mathsf {BV} $, $\mathsf {Grav} $ and $\mathsf …
Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves
S Merkulov, T Willwacher - arXiv preprint arXiv:1511.07808, 2015 - arxiv.org
We establish a new and surprisingly strong link between two previously unrelated theories:
the theory of moduli spaces of curves ${\mathcal M} _ {g, n} $(which, according to Penner, is …
the theory of moduli spaces of curves ${\mathcal M} _ {g, n} $(which, according to Penner, is …
Oriented hairy graphs and moduli spaces of curves
A Andersson, T Willwacher, M Zivkovic - arXiv preprint arXiv:2005.00439, 2020 - arxiv.org
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 …
complex comes in particular with a map to the ribbon graph complex computing the …
The heptagon-wheel cocycle in the Kontsevich graph complex
R Buring, AV Kiselev, NJ Rutten - Journal of Nonlinear Mathematical …, 2017 - Springer
The real vector space of non-oriented graphs is known to carry a differential graded Lie
algebra structure. Cocycles in the Kontsevich graph complex, expressed using formal sums …
algebra structure. Cocycles in the Kontsevich graph complex, expressed using formal sums …
Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs
M Živković - arXiv preprint arXiv:1703.09605, 2017 - arxiv.org
We construct a direct quasi-isomorphism from Kontsevich's graph complex GC_n to the
oriented graph complex OGC_ {n+ 1}, thus providing an alternative proof that the two …
oriented graph complex OGC_ {n+ 1}, thus providing an alternative proof that the two …