An extension of the LMO functor

Cheptea, Habiro and Massuyeau constructed the LMO functor, which is defined on a certain category of cobordisms between two surfaces with at most one boundary component. In this paper, we extend the LMO functor to the case of any number of boundary components, and our functor reflects relations amon...

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Bibliographic Details
Published inGeometriae dedicata Vol. 185; no. 1; pp. 271 - 306
Main Author Nozaki, Yuta
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2016
Springer Nature B.V
Subjects
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Invariants
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
Cobordism
57M27
LMO functor/invariant
Milnor invariant
57M25
Finite-type invariant
Tangle
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Summary:Cheptea, Habiro and Massuyeau constructed the LMO functor, which is defined on a certain category of cobordisms between two surfaces with at most one boundary component. In this paper, we extend the LMO functor to the case of any number of boundary components, and our functor reflects relations among the parts corresponding to the genera and boundary components of surfaces. We also discuss a relationship with finite-type invariants and Milnor invariants.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-016-0176-y