Automorphisms of the compression body graph

Let S be a closed, orientable surface. We show that the automorphism group of the compression body graph of S is the (extended) mapping class group Mod(S). Here, vertices are compression bodies with exterior boundary S, and edges connect compression bodies when one can be realized as a submanifold of the other.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136257/1/jlms12011_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136257/2/jlms12011.pd

Tightness and efficiency of irreducible automorphisms of handlebodies

Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism so that it is most efficient (has minimal growth rate) in its isotopy class. We describe a property, called tightness, of certain invariant laminations, which we conjecture characterizes this efficiency. We obtain partial results towards proving the conjecture. For example, we prove it for genus two handlebodies. We also show that tightness always implies efficiency. In addition, partly in order to provide counterexamples in our study of properties of invariant laminations, we develop a method for generating a class of irreducible automorphisms of handlebodies.Comment: This is the version published by Geometry & Topology on 4 March 200

Symmetry-breaking Answer Set Solving

In the context of Answer Set Programming, this paper investigates symmetry-breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We propose a reduction of disjunctive logic programs to a coloured digraph such that permutational symmetries can be constructed from graph automorphisms. Symmetries are then broken by introducing symmetry-breaking constraints. For this purpose, we formulate a preprocessor that integrates a graph automorphism system. Experiments demonstrate its computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other Computing Paradig