On a homotopy relation between the 2-local geometry and the Bouc complex for the sporadic group Co3

We study the homotopy relation between the standard 2-local geometry and the Bouc complex for the sporadic group Co3. We also give a result concerning the relative projectivity of the reduced Lefschetz module associated to the aformentioned 2-local geometry.Comment: 20 page

Sheaf homology and complete reducibility

AbstractIn the study of finite simple groups by means of the geometries provided by their local subgroups, problems of structure often reduce to questions about modular representations in finite characteristic. Of particular interest are modules spanned by fixed points of Sylow groups (including “high weight” modules for Chevalley groups) for which the homology methods of Ronan and Smith [6]can be very useful. This note presents an elementary sufficient condition for splitting of some reducible modules of this type. Among the applications, we generalize a number of results appearing in recent work of Timmesfeld [11], which provided the original inspiration for this analysis. Some of the ideas had appeared, in a special case, in [10]

On a homotopy relation between the 2-local geometry and the Bouc complex for the sporadic group McL

We study the homotopy relation between the standard 2-local geometry and the Bouc complex for the sporadic finite simple group McL.Comment: 8 pages, 2 tables, final version to appear in Archiv der Mathemati

The monodromy of T-folds and T-fects

We construct a class of codimension-2 solutions in supergravity that realize T-folds with arbitrary $O(2,2,\mathbb{Z})$ monodromy and we develop a geometric point of view in which the monodromy is identified with a product of Dehn twists of an auxiliary surface $\Sigma$ fibered on a base $\mathcal{B}$. These defects, that we call T-fects, are identified by the monodromy of the mapping torus obtained by fibering $\Sigma$ over the boundary of a small disk encircling a degeneration. We determine all possible local geometries by solving the corresponding Cauchy-Riemann equations, that imply the equations of motion for a semi-flat metric ansatz. We discuss the relation with the F-theoretic approach and we consider a generalization to the T-duality group of the heterotic theory with a Wilson line.Comment: 60 pages, 12 figure

Groups and Geometries

[no abstract available

Large subgroups of simple groups

Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies the bound $|H|^3 \ge |G|$. In this note we determine all the large maximal subgroups of finite simple groups, and we establish an analogous result for simple algebraic groups (in this context, largeness is defined in terms of dimension). An application to triple factorisations of simple groups (both finite and algebraic) is discussed.Comment: 37 page

New collections of p-subgroups and homology decompositions for classifying spaces of finite groups

Let G be a finite group and p a prime dividing its order. We define new collections of p-subgroups of G. We study the homotopy relations among them and with the standard collections of p-subgroups. We determine their ampleness and sharpness properties.Comment: 14 pages, some revisions made, final version to appear in Communications in Algebr