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Iis Sinplicial Complexes
III Groups or Rings with Differential 0perators
7 other sections not shown
abelian group abstract simplicial complex Alexander grating allowed homomorphism allowed subgroup barycentric subdivision boundary closed set coboundary Coch cocycle cohomology group cohomology ring compact closure compact subset consider continuous mapping continuous partition coordinates corresponding coset cosimplices covering of finite define definition degree zero derived group differential forms differential operator dimension zero direct sum element of G elements of finite endomorphism exists factor group finite character finite cochains finite number finite order free group given gives graded group graded ring group G group of cochains group with differential hence homology homotopy operator identified integers inverse image isomorphic kernel Let F linear mapping locally compact space natural covering natural homomorphism neighborhood number of simplices open covering open set ordered simplices paracompact partition of unity permutation phism polytope Proof prove sequence simplex simplicial map singular cochains singular simplices tensor product Theorem topological dimension topological space vertex vertices