Autohomeomorphism groups of spaces with unique non-isolated point
Given a uniquely 2-divisible group , we study a commutative loop which arises as a result of a construction in “Engelsche elemente noetherscher gruppen” (1957) by R. Baer. We investigate some general properties and applications of “” and determine a necessary and sufficient condition on in order for to be Moufang. In “A class of loops categorically isomorphic to Bruck loops of odd order” (2014) by M. Greer, it is conjectured that is metabelian if and only if is an automorphic loop. We...
We show that it is possible in rather general situations to obtain a finite-dimensional modular representation of the Galois group of a number field as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over , provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification...