Differentials on graph complexes II: hairy graphs

Anton Khoroshkin; Thomas Willwacher; Marko Živković

doi:10.1007/s11005-017-0964-9

Differentials on graph complexes II: hairy graphs

Anton Khoroshkin, Thomas Willwacher, Marko Živković

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Pages (from-to)	1781-1797
Number of pages	17
Journal	Letters in Mathematical Physics
Volume	107
Issue number	10
DOIs	https://doi.org/10.1007/s11005-017-0964-9
State	Published - 1 Oct 2017
Externally published	Yes

Keywords

Embedding calculus
Graph complexes
Operads

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-017-0964-9

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title = "Differentials on graph complexes II: hairy graphs",

abstract = "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.",

keywords = "Embedding calculus, Graph complexes, Operads",

author = "Anton Khoroshkin and Thomas Willwacher and Marko {\v Z}ivkovi{\'c}",

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doi = "10.1007/s11005-017-0964-9",

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AU - Willwacher, Thomas

AU - Živković, Marko

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Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Embedding calculus

KW - Graph complexes

KW - Operads

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DO - 10.1007/s11005-017-0964-9

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JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 10

ER -

Differentials on graph complexes II: hairy graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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