382 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Kyoto UniversityJP369 papers
- The University of TokyoJP33 papers
- Korea Institute for Advanced StudyKR13 papers
- The University of OsakaJP12 papers
- Centre National de la Recherche ScientifiqueFR10 papers
- Nagoya UniversityJP10 papers
- Seoul National UniversityKR10 papers
- Yukawa Institute for Theoretical PhysicsJP10 papers
- Fujian Normal UniversityCN8 papers
- Kavli Institute for the Physics and Mathematics of the UniverseJP8 papers
- National Research University Higher School of EconomicsRU8 papers
- Hiroshima UniversityJP7 papers
37 papers · 1 filter
Splitting formulas for the rational lift of the Kontsevich integral
Delphine Moussard
Kricker defined an invariant of knots in homology 3-spheres which is a rational lift of the Kontsevich integral, and proved with Garoufalidis that this invariant satisfies splittin…
A homological representation formula of colored Alexander invariants
Tetsuya Ito
We give a formula of the colored Alexander invariant in terms of the homological representation of the braid groups which we call truncated Lawrence's representation. This formula…
On a structure of random open books and closed braids
Tetsuya Ito
A result of Malyutin shows that a random walk on the mapping class group gives rise to an element whose fractional Dehn twist coefficient is large or small enough. We show that thi…
Unified quantum invariants for integral homology spheres associated with simple Lie algebras
Kazuo Habiro, Thang T. Q. Lê
For each finite dimensional, simple, complex Lie algebra and each root of unity (with some mild restriction on the order) one can define the Witten-Reshetikhin-Tu…
The universal sl_2 invariant and Milnor invariants
Jean-Baptiste Meilhan, Sakie Suzuki
The universal sl_2 invariant of string links has a universality property for the colored Jones polynomial of links, and takes values in the h-adic completed tensor powers of the qu…
Kirby calculus for null-homologous framed links in 3-manifolds
Kazuo Habiro, Tamara Widmer
A theorem of Kirby gives a necessary and sufficient condition for two framed links in S^3 to yield orientation-preserving diffeomorphic results of surgery. Kirby's theorem is an im…
A kernel of a braid group representation yields a knot with trivial knot polynomials
Tetsuya Ito
We show that a non-trivial, non-central normal subgroup of the braid groups contains a braid whose closure is a hyperbolic knot with arbitrary large genus. This shows that non-fait…
Overtwisted discs in planar open books
Tetsuya Ito, Keiko Kawamuro
Using open book foliations we show that an overtwisted disc in a planar open book can be put in a topologically nice position. As a corollary, we prove that a planar open book whos…
An invariant of rational homology 3-spheres via vector fields
Tatsuro Shimizu
We define an invariant of rational homology 3-spheres via vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston inv…
Operations on open book foliations
Tetsuya Ito, Keiko Kawamuro
We study b-arc foliation change and exchange move of open book foliations which generalize the corresponding operations in braid foliation theory. We also define a bypass move as a…
Bing doubling and the colored Jones polynomial
Sakie Suzuki
Bing doubling is an operation which gives a satellite of a knot. It is also applied to a link by specifying a component of the link. We give a formula to compute the reduced colore…
On surface links whose link groups are abelian
Tetsuya Ito, Inasa Nakamura
We study surface links whose link groups are free abelian, and construct various stimulating and highly non-trivial examples of such surface links.
On Kirby calculus for null-homotopic framed links in 3-manifolds
Kazuo Habiro, Tamara Widmer
Kirby proved that two framed links in S^3 give orientation-preserving homeomorphic results of surgery if and only if these two links are related by a sequence of two kinds of moves…
A plug with infinite order and some exotic 4-manifolds
Motoo Tange
Every exotic pair in 4-dimension is obtained each other by twisting a {\it cork} or {\it plug} which are codimension 0 submanifolds embedded in the 4-manifolds. The twist was an in…
Open Book Foliations
Tetsuya Ito, Keiko Kawamuro
We study open book foliations on surfaces in 3-manifolds, and give applications to contact geometry of dimension 3. We prove a braid-theoretic formula of the self-linking number of…
On the colored Jones polynomials of ribbon links, boundary links and Brunnian links
Sakie Suzuki
Habiro gave principal ideals of Z[q,q^{-1}] in which certain linear combinations of the colored Jones polynomials of algebraically-split links take values. The author proved that t…
On the universal sl_2 invariant of Brunnian bottom tangles
Sakie Suzuki
A link L is called Brunnian if every proper sublink of L is trivial. Similarly, a bottom tangle T is called Brunnian if every proper subtangle of T is trivial. In this paper, we gi…
Homology cylinders of higher-order
Takahiro Kitayama
We study algebraic structures of certain submonoids of the monoid of homology cylinders over a surface and the homology cobordism groups, using Reidemeister torsion with non-commut…
Non-left-orderable double branched coverings
Tetsuya Ito
We develop a method to show the fundamental group of the double branched covering of a link is not left-orderable by introducing the notion of the coarse presentation. As in the us…
On the universal sl_2 invariant of boundary bottom tangles
Sakie Suzuki
The universal sl_2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. Habiro conjectured that the universal sl_2 invariant of bounda…
Triple linking numbers and triple point numbers of certain -links
Inasa Nakamura
The triple linking number of an oriented surface link was defined as an analogical notion of the linking number of a classical link. We consider a certain -component -link…
The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant
Takahito Kuriya, Thang T. Q. Le, Tomotada Ohtsuki
We show that the perturbative invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra , i.e, the LMO inva…
From mapping class groups to monoids of homology cobordisms: a survey
Kazuo Habiro, Gwenael Massuyeau
Let S be a compact oriented surface. A homology cobordism of S is a cobordism C between two copies of S, such that both the "top" inclusion and the "bottom" inclusion of S in C ind…
On the universal sl_2 invariant of ribbon bottom tangles
Sakie Suzuki
A bottom tangle is a tangle in a cube consisting of arc components whose boundary points are on a line in the bottom square of the cube. A ribbon bottom tangle is a bottom tangle w…