When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings ...When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings with artinian primitive factors.展开更多
This is a brief account of a study leading to the following result: Theorem. For any finite polyhedron K with curvature【0, Wh （π<sub>1</sub>k×z<sup>i</sup>）=0, i≥0. The study is relat...This is a brief account of a study leading to the following result: Theorem. For any finite polyhedron K with curvature【0, Wh （π<sub>1</sub>k×z<sup>i</sup>）=0, i≥0. The study is related to the following theories: S-Cobordism Theorem. Let W be h-cobordism over M<sup>n</sup>, n≥5. Then W is a展开更多
In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A ...In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.展开更多
The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×...The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×S2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S1and Y×S1are diffeomorphic and non-deformation equivalent in cosymplectic sense.展开更多
基金This research is supported by the National Natural Science Foundation of China (19801012)the Ministry of Education of China([2000]65)
文摘When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings with artinian primitive factors.
文摘This is a brief account of a study leading to the following result: Theorem. For any finite polyhedron K with curvature【0, Wh （π<sub>1</sub>k×z<sup>i</sup>）=0, i≥0. The study is related to the following theories: S-Cobordism Theorem. Let W be h-cobordism over M<sup>n</sup>, n≥5. Then W is a
文摘In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.
基金supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education(Grant No.2013004848)
文摘The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×S2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S1and Y×S1are diffeomorphic and non-deformation equivalent in cosymplectic sense.
