论文标题
莫尔斯·诺维科夫（Morse-Novikov）
Morse-Novikov cohomology on foliated manifolds
论文作者
论文摘要
Lichnerowicz或莫尔斯·诺维科夫（Morse-Novikov）的歧管的概念已被许多研究人员用于研究歧管的重要属性和不变性。 Morse-Novikov共同体是使用微分$d_Ω= D+ω\ wedge $定义的，其中$ω$是封闭的$ 1 $ - form。我们研究了莫尔斯·诺维科夫（Morse-Novikov）的共同体学相对于歧管及其同质遗传不变性的叶面，然后将其扩展到riemannian叶片上的更一般的形式。我们研究了相应的差异算子在叶叶莫尔斯 - 诺维科夫复合物上的相应差分算子的Laplacian和Hodge分解。就Riemannian叶子而言，我们证明了减少的叶莫尔斯·诺维科夫同胞组满足了Hodge定理和Poincar {é}二元性。由此产生的异构形成产生hodge钻石结构，用于叶莫尔斯·诺维科夫的同胞。
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 $d_ω=d+ω\wedge$, 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 Poincar{é} duality. The resulting isomorphisms yield a Hodge diamond structure for leafwise Morse-Novikov cohomology.
