A classical fact is that Seifert manifolds with non-empty
boundary are covered by
surface bundles over the circle S1
and closed Seifert manifolds may or may not be
covered by surface bundles over S1. Some closed
graph manifolds are not covered by
surface bundles over S1
([LW] and [N]). Thurston asked if
complete hyperbolic 3-manifolds of finite volume are covered by surface
bundles
[T]. J. Luecke and Y. Wu
asked if graph manifolds with non-empty boundary are covered by surface
bundles
over S1 ([LW]). In this paper we
prove:THEOREM 0·1. Each graph manifold with non-empty
boundary
is finitely covered by a surface bundle over the circle S1.
A new method of surface heparinizing biodegradable polymers was designed. A heparin-modified poly(L-lactic acid) (PLLA) system was developed by physically entrapping the heparin on the PLLA surface. The surface characterization and biological performance of these materials were carried out by SEM, attenuated-total-reflection spectroscopy, contact angle measurements, and platelet adhesion evaluations. The modification strategy was performed by reversible swelling of the PLLA surface following exposure to a solvent–nonsolvent mixture. This process resulted in the localized physical entrapment of the diffused heparin. X-ray photoelectron spectroscopy was used to confirm that control over the heparin surface density can be achieved by using set polymer treatment times. Platelet adhesion tests showed significant improvement in blood compatibility by the PLLA surfaces after modification.
Abstract. W.Thurston raised the following question in 1976: Suppose that a compact 3-manifold M is not covered by (surface)×S 1 or a torus bundle over S 1 . If M 1 and M 2 are two homeomorphic finite covering spaces of M , do they have the same covering degree?For so called geometric 3-manifolds (a famous conjecture is that all compact orientable 3-manifolds are geometric), it is known that the answer is affirmative if M is not a non-trivial graph manifold.In this paper, we prove that the answer for non-trivial graph manifolds is also affirmative. Hence the answer for the Thurston's question is complete for geometric 3-manifolds. Some properties of 3-manifold groups are also derived.Mathematics Subject Classification (1991). 15A18, 15A24, 20F32, 57M10, 57M25.
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