An extension of the LMO functor

Nozaki, Yuta

doi:10.1007/s10711-016-0176-y

Cited by 2 publications

(2 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…AA is a linear symmetric monoidal category extending both " A and the linear version of A mentioned in Remark 3.5, and, similarly, ts AA extends both ts A and this linear version of A. We remark that the extension of Z to LCobT q also generalizes Nozaki's extension of the LMO functor to Lagrangian cobordisms of punctured surfaces [50].…”

Section: Perspectivesmentioning

confidence: 63%

The Kontsevich integral for bottom tangles in handlebodies

Habiro,

Massuyeau

2017

Preprint

View full text Add to dashboard Cite

The Kontsevich integral is a powerful link invariant, taking values in spaces of Jacobi diagrams. In this paper, we extend the Kontsevich integral to construct a functor on the category of bottom tangles in handlebodies. This functor gives a universal finite type invariant of bottom tangles, and refines a functorial version of the Le-Murakami-Ohtsuki 3-manifold invariant for Lagrangian cobordisms of surfaces. Contents 1. Introduction 1 2. The category B of bottom tangles in handlebodies 11 3. Review of the Kontsevich integral 13 4. The category A of Jacobi diagrams in handlebodies 19 5. Presentation of the category A 31 6. A ribbon quasi-Hopf algebra in " A 43 7. Weight systems 47 8. Construction of the functor Z 48 9. The braided monoidal functor Z ϕ q and computation of Z 55 10. Universality of the extended Kontsevich integral 64 11. Relationship with the LMO functor 70 12. Perspectives 78 References 80

show abstract

Section: Perspectivesmentioning

confidence: 63%

The Kontsevich integral for bottom tangles in handlebodies

Habiro,

Massuyeau

2017

Preprint

View full text Add to dashboard Cite

show abstract

“…The former are contained in the "tree reduction" of the LMO functor [5], while the latter are contained in the "tree reduction" of the Kontsevich integral [8]. It seems possible to describe diagrammatically the generalized Johnson homomorphisms τ i m for any g, p ≥ 0 and to relate them to the "tree reduction" of the extended LMO functor introduced in [27]. Example 10.13.…”

Section: Two Types Of Series Associated With Pairs Of Groupsmentioning

confidence: 99%

Generalized Johnson homomorphisms for extended N-series

Habiro

Massuyeau

2018

Journal of Algebra

View full text Add to dashboard Cite

The Johnson filtration of the mapping class group of a compact, oriented surface is the descending series consisting of the kernels of the actions on the nilpotent quotients of the fundamental group of the surface. Each term of the Johnson filtration admits a Johnson homomorphism, whose kernel is the next term in the filtration. In this paper, we consider a general situation where a group acts on a group with a filtration called an extended N-series. We develop a theory of Johnson homomorphisms in this general setting, including many known variants of the original Johnson homomorphisms as well as several new variants.

show abstract

An extension of the LMO functor

Cited by 2 publications

References 31 publications

The Kontsevich integral for bottom tangles in handlebodies

The Kontsevich integral for bottom tangles in handlebodies

Generalized Johnson homomorphisms for extended N-series

Contact Info

Product

Resources

About