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СЕМИНАРЫ |
Семинар по геометрической топологии
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Limit of colimits versus colimit of limits С. А. Мелихов |
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Аннотация: The cohomology of an infinite simplicial complex is generally different from the limit of the cohomology of its finite subcomplexes. As shown by Milnor, the difference is measured by lim Here is the plan (probably, for more than one talk): 0) Some basics (lim, colim, lim 1) A new functor lim 2) A uniqueness theorem for axiomatic homology and cohomology of Polish spaces (=separable complete metric spaces), which is a common generalization of two old uniqueness theorems by Milnor (for axiomatic homology and cohomology of infinite simplicial complexes and of compact metric spaces). The proof of the theorem provides a combinatorial description of homology and cohomology of Polish spaces, in terms of simplicial chain complexes which satisfy lim colim = colim lim. 3) A correction of the functors lim 4) A common correction of strong shape and compactly generated strong shape (which differ from each other essentially by permuting a limit with a colimit) of Polish spaces, which takes into account the topology on the indexing sets.
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