The purpose of this paper is to simplify the computations of the nor-mal bordism groups Ω<sub>i</sub>（W<sub>f</sub>,M×P<sup>∞</sup>;（?））and Ω<sub>i</sub>（C&...The purpose of this paper is to simplify the computations of the nor-mal bordism groups Ω<sub>i</sub>（W<sub>f</sub>,M×P<sup>∞</sup>;（?））and Ω<sub>i</sub>（C<sub>f</sub>,（?）w;θ<sub>f</sub>）which Salomonsenand Dax introduced respectively to study the existence and isotopy classificationof differential embeddings of manifolds in manifolds in the metastable range.Asimpler space pair（K<sub>f</sub>,M×P<sup>∞</sup>）is constructed to replace（W<sub>f</sub>,M×P<sup>∞</sup>）.It isshown that（K<sub>f</sub>,M×P<sup>∞</sup>）is homotopy equivalent to（W<sub>f</sub>,M×P<sup>∞</sup>）and homotopy（n-1）-equivalent to（C<sub>f</sub>,（?）W）.To demonstrate the efficacy of this simplification,the isotopy groups [M<sup>n</sup>（?）RP<sup>n+k</sup>],if n（?）2k-4 and M<sup>n</sup> is a closed（n-k+2）-connected manifold,and[M<sup>n</sup>（?）L（p;q<sub>1</sub>…,q<sub>m</sub>）],if 3n（?）4m-2,M<sup>n</sup> is a closed（2n-2m+1）-connected manifold and L is a （2m+1）-dimensional lens space,arespecifically computed.展开更多
We prove that the n<sup>th</sup> framing bordism group of framed immersed submanifoldsin a manifold N,which is denoted by Δ<sub>n</sub>（N）,is canonically isomorphic to the normalbordism gro...We prove that the n<sup>th</sup> framing bordism group of framed immersed submanifoldsin a manifold N,which is denoted by Δ<sub>n</sub>（N）,is canonically isomorphic to the normalbordism group Ω<sub>n</sub>（N,-TN）.展开更多
In this paper we investigate in detail the Koschorke normal bordism sequence which is very important in application, give a general method by which one may determine the group structures of Ω_1(X, ω) and Ω_2(X, φ)...In this paper we investigate in detail the Koschorke normal bordism sequence which is very important in application, give a general method by which one may determine the group structures of Ω_1(X, ω) and Ω_2(X, φ) appearing in the sequence and compute Ω_i(X×BO(2), φ×Γ), i=1, 2.展开更多
Ⅰ. INTRODUCTIONThroughout this note all manifolds are assumed to be compact,connected and differentiable. A theorem of Rohlin asserts that the first Pontrjagin class of a 4-manifold M is congruent to zero modulo 48, ...Ⅰ. INTRODUCTIONThroughout this note all manifolds are assumed to be compact,connected and differentiable. A theorem of Rohlin asserts that the first Pontrjagin class of a 4-manifold M is congruent to zero modulo 48, provided w<sub>1</sub>（M）=w<sub>2</sub> （M）=0. This result has been generalized to higher dimensions by Milnor and Kervaire.展开更多
文摘The purpose of this paper is to simplify the computations of the nor-mal bordism groups Ω<sub>i</sub>（W<sub>f</sub>,M×P<sup>∞</sup>;（?））and Ω<sub>i</sub>（C<sub>f</sub>,（?）w;θ<sub>f</sub>）which Salomonsenand Dax introduced respectively to study the existence and isotopy classificationof differential embeddings of manifolds in manifolds in the metastable range.Asimpler space pair（K<sub>f</sub>,M×P<sup>∞</sup>）is constructed to replace（W<sub>f</sub>,M×P<sup>∞</sup>）.It isshown that（K<sub>f</sub>,M×P<sup>∞</sup>）is homotopy equivalent to（W<sub>f</sub>,M×P<sup>∞</sup>）and homotopy（n-1）-equivalent to（C<sub>f</sub>,（?）W）.To demonstrate the efficacy of this simplification,the isotopy groups [M<sup>n</sup>（?）RP<sup>n+k</sup>],if n（?）2k-4 and M<sup>n</sup> is a closed（n-k+2）-connected manifold,and[M<sup>n</sup>（?）L（p;q<sub>1</sub>…,q<sub>m</sub>）],if 3n（?）4m-2,M<sup>n</sup> is a closed（2n-2m+1）-connected manifold and L is a （2m+1）-dimensional lens space,arespecifically computed.
文摘We prove that the n<sup>th</sup> framing bordism group of framed immersed submanifoldsin a manifold N,which is denoted by Δ<sub>n</sub>（N）,is canonically isomorphic to the normalbordism group Ω<sub>n</sub>（N,-TN）.
文摘In this paper we investigate in detail the Koschorke normal bordism sequence which is very important in application, give a general method by which one may determine the group structures of Ω_1(X, ω) and Ω_2(X, φ) appearing in the sequence and compute Ω_i(X×BO(2), φ×Γ), i=1, 2.
文摘Ⅰ. INTRODUCTIONThroughout this note all manifolds are assumed to be compact,connected and differentiable. A theorem of Rohlin asserts that the first Pontrjagin class of a 4-manifold M is congruent to zero modulo 48, provided w<sub>1</sub>（M）=w<sub>2</sub> （M）=0. This result has been generalized to higher dimensions by Milnor and Kervaire.
