Topology of moduli spaces of tropical curves with marked points
This article is a sequel to [14]. We study a space g, n of genus g stable, n-marked tropical
curves with total edge length 1. Its rational homology is identified with both top-weight …
curves with total edge length 1. Its rational homology is identified with both top-weight …
Top weight cohomology of moduli spaces of Riemann surfaces and handlebodies
L Hainaut, D Petersen - arXiv preprint arXiv:2305.03046, 2023 - arxiv.org
We show that a certain locus inside the moduli space $ M_g $ of hyperbolic surfaces, given
by surfaces with" sufficiently many" short geodesics, is a classifying space of the handlebody …
by surfaces with" sufficiently many" short geodesics, is a classifying space of the handlebody …
A Serre spectral sequence for the moduli space of tropical curves
We construct, for all $ g\geq 2$ and $ n\geq 0$, a spectral sequence of rational $ S_n $-
representations which computes the $ S_n $-equivariant reduced rational cohomology of …
representations which computes the $ S_n $-equivariant reduced rational cohomology of …
[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 …
Commutative hairy graphs and representations of
V Turchin, T Willwacher - Journal of Topology, 2017 - Wiley Online Library
We express the hairy graph complexes computing the rational homotopy groups of long
embeddings (modulo immersions) of R m in R n as 'decorated'graph complexes associated …
embeddings (modulo immersions) of R m in R n as 'decorated'graph complexes associated …
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 …
Grothendieck-Teichmüller group, operads and graph complexes: a survey
S Merkulov - arXiv preprint arXiv:1904.13097, 2019 - arxiv.org
arXiv:1904.13097v3 [math.QA] 18 Jul 2021 Page 1 arXiv:1904.13097v3 [math.QA] 18 Jul
2021 GROTHENDIECK-TEICHMULLER GROUP, OPERADS AND GRAPH COMPLEXES: A …
2021 GROTHENDIECK-TEICHMULLER GROUP, OPERADS AND GRAPH COMPLEXES: A …
Little disks operads and Feynman diagrams
T Willwacher - Proceedings of the International Congress of …, 2018 - World Scientific
The little disks operads are classical objects in algebraic topology which have seen a wide
range of applications in the past. For example they appear prominently in the Goodwillie …
range of applications in the past. For example they appear prominently in the Goodwillie …
Multi-directed graph complexes and quasi-isomorphisms between them II: Sourced graphs
M Živković - International Mathematics Research Notices, 2021 - academic.oup.com
We prove that the projection from graph complex with at least one source to oriented graph
complex is a quasi-isomorphism, showing that homology of the “sourced” graph complex is …
complex is a quasi-isomorphism, showing that homology of the “sourced” graph complex is …
On the homotopy type of the spaces of spherical knots in
V Turchin, T Willwacher - arXiv preprint arXiv:2012.09965, 2020 - arxiv.org
We study the spaces of embeddings $ S^ m\hookrightarrow R^ n $ and those of long
embeddings $ R^ m\hookrightarrow R^ n $, ie embeddings of a fixed behavior outside a …
embeddings $ R^ m\hookrightarrow R^ n $, ie embeddings of a fixed behavior outside a …