We continue studying the class of modules having reducible complexity over a local ring. In particular, a method is provided for computing an upper bound of the complexity of such a module, in terms of vanishing of certain cohomology modules. We then specialize to complete intersections, which are precisely the rings over which all modules have finite complexity.

We show that the distance between a finite filling slope and a reducible filling slope on the boundary of a hyperbolic knot manifold is at most one. Let M be a knot manifold, i.e. a connected, compact, orientable 3-manifold whose boundary is a torus. A knot manifold is said to be hyperbolic if its interior admits a complete hyperbolic metric of finite volume. Let M(α) denote the manifold obtain...

For any projective curve X let M d (X) be the Simpson moduli space of pure dimension one rank 1 degree d sheaves that are semistable with respect to a fixed polarization H on X . When X is a reduced curve the connected component of M d (X) that contains semistable line bundles can be considered as the compactified Jacobian of X . In this paper we give explicitly the structure of this compactifi...

A finite group G is said to be simply reducible (SR-group) if it has the following two properties: 1) each element of G is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of G with multiplicities not exceeding 1. It is proved that a finite SR-group is solvable if it has no composition factors isomorph...

Rational automorphisms of products of simple p-compact groups are shown to be composites of products of rational automorphisms of the individual factors and permutation maps.

Zn/AcOH on silica gel converts a range of structurally different sulfoxides to their corresponding thioethers in excellent yields under microwave irradiation. It has been found that chemoselective deoxygenation of sufoxides can be achieved in the presence of other reducible functional groups such as acetals, acids, amides,   esters, ketones and nitriles.  

In this paper, we study the class of of C3-like Finsler metrics which contains the class of semi-C-reducible Finsler metric. We find a condition on C3-like metrics under which the notions of Landsberg curvature and mean Landsberg curvature are equivalent.