叶状流形上的莫尔斯-诺维科夫同调

IF 0.6 4区 数学 Q3 MATHEMATICS
Md. Shariful Islam
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引用次数: 0

摘要

许多研究人员利用流形的 Lichnerowicz 或 Morse-Novikov 同调群这一概念来研究流形的重要性质和不变量。莫尔斯-诺维科夫同调是用微分 dω=d+ω∧ 来定义的,其中 ω 是一个封闭的 1-形式。我们研究了相对于流形上的扇形的莫尔斯-诺维科夫同调及其同调不变性,然后将其扩展到黎曼扇形上的更一般类型的形式。我们研究了还原叶向莫尔斯-诺维科夫复数上相应微分算子的拉普拉斯和霍奇分解。在黎曼叶面的情况下,我们证明了还原叶向莫尔斯-诺维科夫同调群满足霍奇定理和庞加莱对偶性。由此产生的同构产生了叶向莫尔斯-诺维科夫同调的霍奇菱形结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Morse-Novikov cohomology on foliated manifolds

The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has been utilized by many researchers to study important properties and invariants of a manifold. Morse-Novikov cohomology is defined using the differential dω=d+ω, where ω is a closed 1-form. We study Morse-Novikov cohomology relative to a foliation on a manifold and its homotopy invariance and then extend it to more general type of forms on a Riemannian foliation. We study the Laplacian and Hodge decompositions for the corresponding differential operators on reduced leafwise Morse-Novikov complexes. In the case of Riemannian foliations, we prove that the reduced leafwise Morse-Novikov cohomology groups satisfy the Hodge theorem and Poincaré duality. The resulting isomorphisms yield a Hodge diamond structure for leafwise Morse-Novikov cohomology.

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来源期刊
CiteScore
1.00
自引率
20.00%
发文量
81
审稿时长
6-12 weeks
期刊介绍: Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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