Cohomology of groups
Cohomology of groups
复制标题
群的上同调
DOI：
10.1007/0-387-32968-4_10
复制
发表时间：
1969
期刊：
影响因子：
--
通讯作者：
E. Weiss
中科院分区：
文献类型：
--
作者：
E. Weiss
设E是一个真实的Hilbert空间，它具有一个内积<·，·>和相应的范数ε·ε，I ∈ C 1（E，R）是一个强不定泛函，i.例如，在有限余维的任何子空间上，I从下到上都是无界的。众所周知，I的任何临界点的莫尔斯指数必然是无穷大。在这种情况下，人们通常不能指望从通常的莫尔斯理论中获得任何有用的信息。为了克服这个困难，需要更先进的理论。在本章的10.1-10.4节中，我们首先介绍W。Kryszewski-A. Szulkin无穷维上同调理论和与之相关的莫尔斯理论（见[200]），然后我们发展了一些方法来精确计算群。应用到哈密顿系统和梁方程将给出。
LetEbe a real Hilbert space with an inner product <·, ·> and associated norm ‖ · ‖, and letI∈C1(E,R) be a strongly indefinite functional, i. e.,Iis unbounded from below and from above on any subspace of finite codimension. It is well known that the Morse index of any critical point of I must necessarily be infinite. In this case usually one can not expect to obtain any useful information from the usual Morse theory. In order to overcome this difficulty, a more advanced theory is needed. In sections 10.1–10.4 of this chapter, we first introduce the W. Kryszewski-A. Szulkin infinite-dimensional cohomology theory and a Morse theory associated with it (see [200]) and then we develop some methods to compute the groups precisely. Applications to Hamiltonian systems and beam equations will be given.