The problem of deciding whether a graph manifold is finitely covered by a surface bundle over the circle is discussed in this paper.A necessary and sufficient condition in term of the solutions of a certain matrix equ...The problem of deciding whether a graph manifold is finitely covered by a surface bundle over the circle is discussed in this paper.A necessary and sufficient condition in term of the solutions of a certain matrix equation is obtained,as well as a necessary condition which is easy to compute. Our results sharpen and extend the earlier results of J.Leucke-Y.Wu,W.Neumann,and S.Wang-F. Yu in this topic.展开更多
We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions...We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions of symmetric Schr?dinger operator, initially defined on a smooth function, whose support does not contain the branch points of the graph and branch points of the manifold. These results are obtained for graphs with a single vertex, graphs with multiple vertices and graphs with a single vertex and countable set of rays.展开更多
文摘The problem of deciding whether a graph manifold is finitely covered by a surface bundle over the circle is discussed in this paper.A necessary and sufficient condition in term of the solutions of a certain matrix equation is obtained,as well as a necessary condition which is easy to compute. Our results sharpen and extend the earlier results of J.Leucke-Y.Wu,W.Neumann,and S.Wang-F. Yu in this topic.
文摘We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions of symmetric Schr?dinger operator, initially defined on a smooth function, whose support does not contain the branch points of the graph and branch points of the manifold. These results are obtained for graphs with a single vertex, graphs with multiple vertices and graphs with a single vertex and countable set of rays.
