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TOPOLOGICAL SYMMETRY GROUPS OF COMPLETE GRAPHS IN THE 3-SPHERE
TOPOLOGICAL SYMMETRY THE 3-SPHERE
2015/12/17
The orientation preserving topological symmetry group of
a graph embedded in the 3-sphere is the subgroup of the automorphism
group of the graph consisting of those automorphisms which can be
induc...
TOPOLOGICAL SYMMETRY GROUPS OF GRAPHS IN 3-MANIFOLDS
GRAPHS IN 3-MANIFOLDS SYMMETRY GROUPS
2015/12/17
We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group An which is not
the topological symmetry group of any graph embedded in the manifold.
...
Hairy graphs and the unstable homology of Mod(g,s), Out(F_n) and Aut(F_n)
Hairy graphs Algebraic Topology
2011/9/20
Abstract: For every cyclic operad O there is an associated Lie algebra hO of positive degree symplectic derivations. For the associative and Lie operads, Kontsevich used his graph homology theory to p...
Combinatorial R-trees as generalized Cayley graphs for fundamental groups of one-dimensional spaces
R-tree generalized Cayley graph one-dimensional space
2011/8/29
Abstract: In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like object that might be considered the topologic...
The Kauffman polynomial and trivalent graphs
braids invariants for graphs and links Kau man polynomial knotted graphs
2011/8/26
Abstract: We construct a state model for the two-variable Kauffman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for trivalent graphs embedded in th...
Abstract: In this paper, we develop a diamond graph theory and apply the theory to the (co)homology of the Lie algebra generated by positive systems of the classical semi-simple Lie algebras over the ...
Upper bounds for the bondage number of graphs on topological surfaces
Bondage number Domination number Topological surface
2011/2/22
The bondage number b(G) of a graph G is the smallest number of edges of G whose removal from G results in a graph having the domination number larger than that of G. We show that, for a graph G having...
The Gauss image of entire graphs of higher codimension and Bernstein type theorems
Gauss image entire graphs of higher codimension Bernstein type theorems
2010/12/9
Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori esti...