23 citations · 257 across the 67 of their papers we have counts for
14 papers · 1 filter
On a group whose generalized torsion elements are torsion elements
Tetsuya Ito
We show that a group whose generalized torsion elements are torsion elements (which we call a -group) is torsion-by- group, an extension of torsion group by a group…
Actions of the n-strand braid groups on the free group of rank n which are similar to the Artin representation
Tetsuya Ito
We classify an action of the -strand braid group on the free group of rank which is similar to the Artin representation in the sense that the -th generator of $B_…
Isolated orderings on amalgamated free products
Tetsuya Ito
We show that an amalgamated free product admits a discrete isolated ordering, under some assumptions of and . This generalizes the author's previous construction…
Garside-theoretic analysis of Burau representations
Matthieu Calvez, Tetsuya Ito
We establish relations between both the classical and the dual Garside structures of the braid group and the Burau representation. Using the classical structure, we formulate a non…
Curve diagram for Artin group of type B
Tetsuya Ito
We develop a theory of curve diagrams for Artin groups of type B. We define the winding number labeling and the wall crossing labeling of curve diagrams, and show that these labeli…
Reading the dual Garside length of braids from homological and quantum representations
Tetsuya Ito
We show that Lawrence's representation and linear representations from quantum sl_2 called generic highest weight vectors detect the dual Garside length of braids in a simple and n…
Lawrence-Krammer-Bigelow representations and dual Garside length of braids
Tetsuya Ito, Bert Wiest
We show that the span of the variable in the Lawrence-Krammer-Bigelow representation matrix of a braid is equal to the twice of the dual Garside length of the braid, as was con…
Construction of isolated left orderings via partially central cyclic amalgamation
Tetsuya Ito
We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups hav…
Dehornoy-like left orderings and isolated left orderings
Tetsuya Ito
We introduce a Dehornoy-like ordering of groups, which is a generalization of the Dehornoy ordering of the braid groups. Under a weak assumption which we call Property F, we show t…
Hurwitz equivalences of positive group generators
Tetsuya Ito
For a positively presented group G, we provide a criterion for two tuples of positive group generators of G to be Hurwitz equivalent or Hurwitz-conjugation equivalent. We also pres…
Space of group orderings, quasi morphisms and bounded cohomology
Tetsuya Ito
For a group , we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflec…
Finite orbits of Hurwitz actions on braid systems
Tetsuya Ito
There are natural actions of the braid groups on the products of the braid groups, called the Hurwitz action. We first study the roots of centralizers in the braid groups. By using…
Finite Thurston type orderings on dual braid monoids
Tetsuya Ito
For a finite Thurston type ordering < of the braid group B_{n}, we introduce a new normal form of a dual positive braid which we call the C-normal form. This normal form extends Fr…
On finite Thurston type orderings of braid groups
Tetsuya Ito
We prove that for any finite Thurston-type ordering on the braid group\ , the restriction to the positive braid monoid is a\ well-ordered set of…