scholarly journals A calculus for ideal triangulations of three-manifolds with embedded arcs

2005 ◽  
Vol 278 (9) ◽  
pp. 975-994 ◽  
Author(s):  
Gennaro Amendola
Keyword(s):  
Ideal Triangulations

scholarly journals A METHOD TO FIND IDEAL POINTS FROM IDEAL TRIANGULATIONS

2010 ◽  
Vol 19 (04) ◽  
pp. 509-524
Author(s):  
YUICHI KABAYA
Keyword(s):  
Linear Algebra ◽  
Character Variety ◽  
Ideal Triangulations ◽  
Ideal Points

We give a method to find ideal points of the character variety of a 3-manifold with toral boundary. This can be easily carried out by using linear algebra.

scholarly journals On minimal ideal triangulations of cusped hyperbolic 3‐manifolds

2020 ◽  
Vol 13 (1) ◽  
pp. 308-342
Author(s):  
William Jaco ◽  
Hyam Rubinstein ◽  
Jonathan Spreer ◽  
Stephan Tillmann
Keyword(s):  
Minimal Ideal ◽  
Ideal Triangulations

Every finite group action on a compact 3-manifold preserves infinitely many hyperbolic spatial graphs

2014 ◽  
Vol 23 (06) ◽  
pp. 1450034 ◽  
Author(s):  
Toru Ikeda
Keyword(s):  
Finite Group ◽  
Group Action ◽  
Group Actions ◽  
Infinite Family ◽  
Finite Group Action ◽  
Finite Group Actions ◽  
Spatial Graph ◽  
Cell Decompositions ◽  
Spatial Graphs ◽  
Ideal Triangulations

We consider symmetries of spatial graphs in compact 3-manifolds described by smooth finite group actions. This paper provides a method for constructing an infinite family of hyperbolic spatial graphs with given symmetry by connecting spatial graph versions of hyperbolic tangles in 3-cells of polyhedral cell decompositions induced from triangulations of the 3-manifolds. This method is applicable also to the case of ideal triangulations.

scholarly journals Minimum ideal triangulations of hyperbolic 3-manifolds

1991 ◽  
Vol 6 (2) ◽  
pp. 135-153 ◽  
Author(s):  
Colin Adams ◽  
William Sherman
Keyword(s):  
Ideal Triangulations

scholarly journals An inequality for polyhedra and ideal triangulations of cusped hyperbolic 3-manifolds

1996 ◽  
Vol 124 (12) ◽  
pp. 3905-3911 ◽  
Author(s):  
Masaaki Wada ◽  
Yasushi Yamashita ◽  
Han Yoshida
Keyword(s):  
Ideal Triangulations

scholarly journals Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials

2012 ◽  
Vol 148 (6) ◽  
pp. 1833-1866 ◽  
Author(s):  
Giovanni Cerulli Irelli ◽  
Daniel Labardini-Fragoso
Keyword(s):  
Linear Independence ◽  
Cluster Algebra ◽  
Arbitrary System ◽  
Triangulated Surfaces ◽  
Jacobian Algebra ◽  
Quiver With Potential ◽  
Ideal Triangulations ◽  
The Given ◽  
Marked Points ◽  
The Ideal

AbstractTo each tagged triangulation of a surface with marked points and non-empty boundary we associate a quiver with potential in such a way that whenever we apply a flip to a tagged triangulation the Jacobian algebra of the quiver with potential (QP) associated to the resulting tagged triangulation is isomorphic to the Jacobian algebra of the QP obtained by mutating the QP of the original one. Furthermore, we show that any two tagged triangulations are related by a sequence of flips compatible with QP-mutation. We also prove that, for each of the QPs constructed, the ideal of the non-completed path algebra generated by the cyclic derivatives is admissible and the corresponding quotient is isomorphic to the Jacobian algebra. These results, which generalize some of the second author’s previous work for ideal triangulations, are then applied to prove properties of cluster monomials, like linear independence, in the cluster algebra associated to the given surface by Fomin, Shapiro and Thurston (with an arbitrary system of coefficients).

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