Virtually splitting the map from Aut(G) to Out(G)

We give an elementary criterion on a group G for the map from Aut(G) to Out(G) to split virtually. This criterion applies to many residually finite CAT(0) groups and hyperbolic groups, and in particular to all finitely generated Coxeter groups. As a consequence the outer automorphism group of any finitely generated Coxeter group is residually finite and virtually torsion-free.Comment: 10 pages, 1 figur

The automorphism group of accessible groups

In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by taking extensions of relative automorphism groups of vertex groups, groups of Dehn twists and groups of automorphisms of free products. We apply this description and obtain a criterion for Out(G) to be finitely presented, as well as a necessary and sufficient condition for Out(G) to be finite. Consequences for hyperbolic groups are discussed.Comment: 18 pages, 3 figures. Section 4 rewritten and corrected, added reference

Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed. Views interconnect these developments and establish that the axiomatizations are equivalent in the sense of being mutually interpretable. A realm also contains an external interface that is convenient for users of the library who want to apply the concepts and facts of the theory without delving into the details of how the concepts and facts were developed. We illustrate the utility of realms through a series of examples. We also give an outline of the mechanisms that are needed to create and maintain realms.Comment: As accepted for CICM 201

Locally compact convergence groups and n-transitive actions

All sigma-compact, locally compact groups acting sharply n-transitively and continuously on compact spaces M have been classified, except for n=2,3 when M is infinite and disconnected. We show that no such actions exist for n=2 and that these actions for n=3 coincide with the action of a hyperbolic group on a space equivariantly homeomorphic to its hyperbolic boundary. We further give a characterization of non-compact groups acting 3-properly and transitively on infinite compact sets as non-elementary boundary transitive hyperbolic groups. The main tool is a generalization to locally compact groups of Bowditch's topological characterization of hyperbolic groups. Finally, in contrast to the case n=3, we show that for n>3, if a locally compact group acts continuously, n-properly and n-cocompactly on a locally connected metrizable compactum M, then M has a local cut point

Isotope shift on the chlorine electron affinity revisited by an MCHF/CI approach

Today, the electron affinity is experimentally well known for most of the elements and is a useful guideline for developing ab initio computational methods. However, the measurements of isotope shifts on the electron affinity are limited by both resolution and sensitivity. In this context, theory eventually contributes to the knowledge and understanding of atomic structures, even though correlation plays a dominant role in negative ions properties and, particularly, in the calculation of the specific mass shift contribution. The present study solves the longstanding discrepancy between calculated and measured specific mass shifts on the electron affinity of chlorine (Phys. Rev. A 51 (1995) 231)Comment: 18 pages, 2 figures, 7 table

SAGA: A DSL for Story Management

Video game development is currently a very labour-intensive endeavour. Furthermore it involves multi-disciplinary teams of artistic content creators and programmers, whose typical working patterns are not easily meshed. SAGA is our first effort at augmenting the productivity of such teams. Already convinced of the benefits of DSLs, we set out to analyze the domains present in games in order to find out which would be most amenable to the DSL approach. Based on previous work, we thus sought those sub-parts that already had a partially established vocabulary and at the same time could be well modeled using classical computer science structures. We settled on the 'story' aspect of video games as the best candidate domain, which can be modeled using state transition systems. As we are working with a specific company as the ultimate customer for this work, an additional requirement was that our DSL should produce code that can be used within a pre-existing framework. We developed a full system (SAGA) comprised of a parser for a human-friendly language for 'story events', an internal representation of design patterns for implementing object-oriented state-transitions systems, an instantiator for these patterns for a specific 'story', and three renderers (for C++, C# and Java) for the instantiated abstract code.Comment: In Proceedings DSL 2011, arXiv:1109.032