scholarly journals The complexity of locally injective homomorphisms

2010 ◽  
Vol 310 (20) ◽  
pp. 2685-2696 ◽  
Author(s):  
Gary MacGillivray ◽  
Jacobus Swarts
Keyword(s):  
Injective Homomorphisms

scholarly journals A FUNCTORIAL APPROACH TO THE C*-ALGEBRAS OF A GRAPH

2002 ◽  
Vol 13 (03) ◽  
pp. 245-277 ◽  
Author(s):  
JACK SPIELBERG
Keyword(s):  
Structural Properties ◽  
Inductive Limit ◽  
Directed Graphs ◽  
Graph Algebras ◽  
C Algebras ◽  
Injective Homomorphisms ◽  
Functorial Approach

A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to the category of C*-algebras with injective *-homomorphisms. The resulting C*-algebras are identified as Toeplitz graph algebras. Graph algebras are proved to have inductive limit decompositions over any family of subgraphs with union equal to the whole graph. The construction is used to prove various structural properties of graph algebras.

scholarly journals Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces

2015 ◽  
Vol 26 (09) ◽  
pp. 1550066 ◽  
Author(s):  
Michael Brandenbursky
Keyword(s):  
Braid Group ◽  
Infinite Family ◽  
Orientable Surface ◽  
Hyperbolic Surface ◽  
Invariant Metrics ◽  
Closed Orientable Surface ◽  
Infinite Dimensional ◽  
Hamiltonian Diffeomorphisms ◽  
Injective Homomorphisms ◽  
Area Preserving

Let Σg be a closed orientable surface of genus g and let Diff 0(Σg, area ) be the identity component of the group of area-preserving diffeomorphisms of Σg. In this paper, we present the extension of Gambaudo–Ghys construction to the case of a closed hyperbolic surface Σg, i.e. we show that every nontrivial homogeneous quasi-morphism on the braid group on n strings of Σg defines a nontrivial homogeneous quasi-morphism on the group Diff 0(Σg, area ). As a consequence we give another proof of the fact that the space of homogeneous quasi-morphisms on Diff 0(Σg, area ) is infinite-dimensional. Let Ham (Σg) be the group of Hamiltonian diffeomorphisms of Σg. As an application of the above construction we construct two injective homomorphisms Zm → Ham (Σg), which are bi-Lipschitz with respect to the word metric on Zm and the autonomous and fragmentation metrics on Ham (Σg). In addition, we construct a new infinite family of Calabi quasi-morphisms on Ham (Σg).

scholarly journals Counting Edge-injective Homomorphisms and Matchings on Restricted Graph Classes

2018 ◽  
Vol 63 (5) ◽  
pp. 987-1026 ◽  
Author(s):  
Radu Curticapean ◽  
Holger Dell ◽  
Marc Roth
Keyword(s):  
Graph Classes ◽  
Injective Homomorphisms

On injective homomorphisms between Teichmüller modular groups I

1999 ◽  
Vol 135 (2) ◽  
pp. 425-486 ◽  
Author(s):  
Nikolai V. Ivanov ◽  
John D. McCarthy
Keyword(s):  
Modular Groups ◽  
Injective Homomorphisms
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