半单复形IM_V(M,Q)(英文)  

A SEMISIMPLICIAL COMPLEX IM_V(M,Q)

作　　者：郭景美[1] 

机构地区：[1]南开大学数学系,天津300071

出　　处：《数学杂志》2003年第4期403-406,共4页Journal of Mathematics

基　　金：SupportedbytheNationaelNaturalSciemceFoundatoonofChina .

摘　　要：设M ,V ,Q是李普希茨流形 ,M是V的局部LIP平坦的紧子流形 ,V是开流形且dimV =dimQ .设U是M在V中的某开邻域且Δn 是Rn 中n维标准单形 .如f:Δn×U→Δn×Q是一个LIP浸入且P1f =P1,称f是一个n维单形 .令 (IMV(m ,Q) ) n 是上面所定义的所有n维单形的集合且令IMV(m ,Q) ={ (IMV(M ,Q) ) n} n 0 .本文证明了IMV(M ,Q)在我们所定义的面运算 i和退化运算Si下是一个半单复形 .Let M,V,Q be Lipschitz manifolds, M be a locally flat and compact submanifold of V, V be an open manifold and dim V =dim Q. And let U be an open neighborhood of M in V and Δ n be the n dimensional standard simplex in R n. if f: Δ n×U→Δ n×Q is a LIP immersion and P 1f=P 1, we call f an n dimensional simplex. Let (IM V(M,Q)) n be the set of all f and IM V(M,Q) ={(IM V(M,Q)) n} n≥0. In this paper, we proved that Im v(M,Q) together with the face operator  i and the degeneracy operater S i defined by us is a semisimplicial complex.

关 键 词：半单复形 李普希茨流形 LIP浸入 

分 类 号：O189.21[理学—数学]