半单复形IMv(M,Q)

摘要

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 △n be the n-dimensional standard simplex in Rn. if f: △n × U→△n × Q is a LIP immersion and P1 f= P1, we call f an n-dimensional simplex. Let (IMv (M, Q))n be the set of all f and IMv(M,Q)={(IMv(M,Q))n}n≥0. In this paper, we proved that Imv(M,Q) together with the face operator (e)i and the degeneracy operater Si defined by us is a semisimplicial complex.%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=dim Q.设U是M在V中的某开邻域且△n是Rn中n维标准单形.如f:△n×U→△n×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(e)i和退化运算Si下是一个半单复形.