The classification of 2-compact groups

We prove that any connected 2-compact group is classified by its 2-adic root datum, and in particular the exotic 2-compact group DI(4), constructed by Dwyer-Wilkerson, is the only simple 2-compact group not arising as the 2-completion of a compact connected Lie group. Combined with our earlier work with Moeller and Viruel for p odd, this establishes the full classification of p-compact groups, stating that, up to isomorphism, there is a one-to-one correspondence between connected p-compact groups and root data over the p-adic integers. As a consequence we prove the maximal torus conjecture, giving a one-to-one correspondence between compact Lie groups and finite loop spaces admitting a maximal torus. Our proof is a general induction on the dimension of the group, which works for all primes. It refines the Andersen-Grodal-Moeller-Viruel methods to incorporate the theory of root data over the p-adic integers, as developed by Dwyer-Wilkerson and the authors, and we show that certain occurring obstructions vanish, by relating them to obstruction groups calculated by Jackowski-McClure-Oliver in the early 1990s.Comment: 47 page

The C*-algebra of an affine map on the 3-torus

We study the C*-algebra of an affine map on a compact abelian group and give necessary and sufficient conditions for strong transitivity when the group is a torus. The structure of the C*-algebra is completely determined for all strongly transitive affine maps on a torus of dimension one, two or three

Reduced, tame and exotic fusion systems

We define here two new classes of saturated fusion systems, reduced fusion systems and tame fusion systems. These are motivated by our attempts to better understand and search for exotic fusion systems: fusion systems which are not the fusion systems of any finite group. Our main theorems say that every saturated fusion system reduces to a reduced fusion system which is tame only if the original one is realizable, and that every reduced fusion system which is not tame is the reduction of some exotic (nonrealizable) fusion system

Face configuration affects speech perception: Evidence from a McGurk mismatch negativity study

AbstractWe perceive identity, expression and speech from faces. While perception of identity and expression depends crucially on the configuration of facial features it is less clear whether this holds for visual speech perception.Facial configuration is poorly perceived for upside-down faces as demonstrated by the Thatcher illusion in which the orientation of the eyes and mouth with respect to the face is inverted (Thatcherization). This gives the face a grotesque appearance but this is only seen when the face is upright.Thatcherization can likewise disrupt visual speech perception but only when the face is upright indicating that facial configuration can be important for visual speech perception. This effect can propagate to auditory speech perception through audiovisual integration so that Thatcherization disrupts the McGurk illusion in which visual speech perception alters perception of an incongruent acoustic phoneme. This is known as the McThatcher effect.Here we show that the McThatcher effect is reflected in the McGurk mismatch negativity (MMN). The MMN is an event-related potential elicited by a change in auditory perception. The McGurk-MMN can be elicited by a change in auditory perception due to the McGurk illusion without any change in the acoustic stimulus.We found that Thatcherization disrupted a strong McGurk illusion and a correspondingly strong McGurk-MMN only for upright faces. This confirms that facial configuration can be important for audiovisual speech perception. For inverted faces we found a weaker McGurk illusion but, surprisingly, no MMN. We also found no correlation between the strength of the McGurk illusion and the amplitude of the McGurk-MMN. We suggest that this may be due to a threshold effect so that a strong McGurk illusion is required to elicit the McGurk-MMN

Automorphisms of p-compact groups and their root data

We construct a model for the space of automorphisms of a connected p-compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer automorphism group of a p-compact group can be lifted to a group action, analogous to a classical theorem of de Siebenthal for compact Lie groups. The model of this paper is used in a crucial way in our paper ``The classification of 2-compact groups'', where we prove the conjectured classification of 2-compact groups and determine their automorphism spaces.Comment: 24 pages. Introduction restructured and title changed (from "Automorphisms of root data, maximal torus normalizers, and p-compact groups"). Various other adjustments mad