Differentials on graph complexes. II: Hairy graphs. (English) Zbl 1373.05216
Summary: We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging to zero whose first pages contain the hairy graph cohomology. Our results yield a way to construct many nonzero hairy graph cohomology classes out of (known) non-hairy classes by studying the cancellations in those sequences. This provide a first glimpse at the tentative global structure of the hairy graph cohomology.
For Part I see [the authors, Adv. Math. 307, 1184–1214 (2017; Zbl 1352.05192)].
For Part I see [the authors, Adv. Math. 307, 1184–1214 (2017; Zbl 1352.05192)].
MSC:
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
| 53D55 | Deformation quantization, star products |
| 18G35 | Chain complexes (category-theoretic aspects), dg categories |
| 57Q45 | Knots and links in high dimensions (PL-topology) (MSC2010) |
Citations:
Zbl 1352.05192References:
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