Let （M; H1, H2; Fo） be a SD-splitting for bordered 3-manifold M. The splitting is reducible （weakly reducible, respectively） if there exist essential disks D1 belong to H1 and D2 belong to H2 such that δD1,δD2 b...Let （M; H1, H2; Fo） be a SD-splitting for bordered 3-manifold M. The splitting is reducible （weakly reducible, respectively） if there exist essential disks D1 belong to H1 and D2 belong to H2 such that δD1,δD2 belong to Fo and δD1 =δD2 （δD1 ∩ δD2 =φ, respectively）. A SD-splitting （M; H1, H2; Fo） for bordered 3-manifold M is of inner genus 1 if Fo is a punctured torus. In the present paper, we show that a weakly reducible SD-splitting of inner genus 1 is either reducible or bilongitudional.展开更多
In the present paper, we characterize the bordered 3-manifolds with genus 1 D-splittings and SD-splittings. We also describe a minimal genus SD-splitting for a handlebody and surface × I.
基金the National Natural Science Foundation of China(10571034)
文摘Let （M; H1, H2; Fo） be a SD-splitting for bordered 3-manifold M. The splitting is reducible （weakly reducible, respectively） if there exist essential disks D1 belong to H1 and D2 belong to H2 such that δD1,δD2 belong to Fo and δD1 =δD2 （δD1 ∩ δD2 =φ, respectively）. A SD-splitting （M; H1, H2; Fo） for bordered 3-manifold M is of inner genus 1 if Fo is a punctured torus. In the present paper, we show that a weakly reducible SD-splitting of inner genus 1 is either reducible or bilongitudional.
基金Work supported in part by a grant (No.10171024) of NSFCa grant of the Outstanding Youth Fellowship of Heilongjiang Province
文摘In the present paper, we characterize the bordered 3-manifolds with genus 1 D-splittings and SD-splittings. We also describe a minimal genus SD-splitting for a handlebody and surface × I.
