On the Novikov complex for rational Morse forms
On the Novikov complex for rational Morse forms
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关于有理莫尔斯形式的诺维科夫复形
DOI：
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发表时间：
1995
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通讯作者：
A. Pajitnov
中科院分区：
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作者：
A. Pajitnov
设W是紧致流形M上具有非退化零点的闭1-形式。假设上同调类[03 C9] E H1（M，IR）是整数直到乘法常数。设p：M-iM是具有结构群G的覆盖，使得p ~（w~ = 0.对于这些数据，我们在ZG的Novikov完成上关联一个自由基复形C*。对于每一个k，Ck的自由生成元的个数等于索引为k的w的零点的个数。C* 的单同伦型等于M的Novikov-完全单纯链复形的单同伦型。
Let w a closed 1-form with non-degenerate zeros on a compact manifold M. Assume that the cohomology class [03C9] E H1 (M, IR) is integral up to a multiplicative constant. Let p : M -i M be a covering with structure group G, such that p ~ (w~ ~ = o. To this data we associate a free based complex C* over the Novikov completion of ZG. For every k the number of free generatores of Ck equals the number of zeros of w of index k. The simple homotopy type of C* equals the simple homotopy type of the Novikov-completed simplicial chain complex of M.