The shock breakout emission is the first light that emerges from a supernova. In spherical case it characterized by brief UV flash. an axisymmetric, non-spherical prolate explosion, breaches surface along symmetry axis, then peels around to larger angles, producing curve which may differ substantially spherically symmetric case. We study emergence of non-relativistic, bipolar star, and estimate...

Let G be a torsion-free hyperbolic group and let n ≥ 6 be an integer. We prove that G is the fundamental group of a closed aspherical manifold if the boundary of G is homeomorphic to an (n − 1)-dimensional sphere.

We investigate asphericity of the relative group presentation 〈G, t | atbtctdtet = 1〉 and prove it aspherical provided the subgroup of G generated by {ab−1, bc−1, cd−1, de−1} is neither finite cyclic nor a finite triangle group. We also prove a similar result for the closely related relative group presentation 〈G, s, t | αsβsγt = 1 = δtεtζs−1〉.

We consider geometric decompositions of aspherical 4-manifolds which fibre over 2-orbifolds. We show that no such manifold admits infinitely many fibrations over hyperbolic base orbifolds and that “most” Seifert fibred 4-manifolds over hyperbolic bases have a decomposition induced from a decomposition of