Abstract. For any n ∈ N we construct graph manifolds of genus 4n that have 3n-generated fundamental group. 1. introduction A Heegaard surface of an orientable closed 3-manifold M is an embedded orientable surface S such that M − S consists of 2 handlebodies V1 and V2. This decomposition of M is called a Heegaard splitting and denoted by M = V1 ∪S V2. We say that the splitting is of genus g if S is of genus g. It is not difficult to see that any orientable closed 3-manifold admits a Heegaard splitting. If M admits a Heegaard splitting of genus g but no Heegaard splitting of smaller genus then we say that M has Heegaard genus g and write g(M) = g. Clearly any curve in a handlebody can be homotoped to its boundary. It follows that for any Heegaard splitting M = V1 ∪S V2 every curve in M can be homotoped into V1. Thus the map induced by the inclusion of V1 into M maps a generating set of π1(V1) to a generating set of π1(M). As π1(V1) is generated by g elements it follows that π1(M) is also generated by g elements. Thus g(M) ≥ r(M) where

We give a classification theorem for unital separable simple nuclear C ∗-algebras with tracial topological rank zero which satisfy the Universal Coefficient Theorem. We prove that if A and B are two such C ∗-algebras and then A ∼ = B.

Abstract not found

processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decompo- sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum

Abstract not found

The Lie Algebra Rank Condition plays a central role in nonlinear systems control theory. We show that the satisfaction of this condition by a set of smooth control vector fields is equivalent to the existence of smooth transverse periodic functions. The proof here outlined details can be found

The controllability condition for right invariant systems on Lie groups derived in [8] was applied to quantum systems in [1], [4], [7]. This condition is called the Lie Algebra Rank Condition. In applications to quantum systems, the condition has been stated assuming that the right invariant

The controllability condition for right invariant systems on Lie groups derived in [7] was applied to quantum systems in [1], [4], [6]. This condition is called the Lie Algebra Rank Condition, and it has been stated assuming that the right invariant differential system under consideration

The goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of L-functions allows one to produce many examples of L-functions over function fields vanishing to high order at the center point of their functional equation

The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts