THE LEFSCHETZ NUMBER OF AN n-VALUED MULTIMAP
THE LEFSCHETZ NUMBER OF AN n-VALUED MULTIMAP
复制标题
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
RobertF Brown
中科院分区：
文献类型：
--
作者：
RobertF Brown
n 值多重映射是连续多值函数 �: X ⊸ Y，使得 �(x) 是 Y 的 n 个点的无序子集（对于每个 x ∈ X）。如果 X 和 Y 是有限多面体，则引入与有理系数同调的分级同态。对于 : X ⊸ X 的莱夫谢茨数 L(�) 被定义为诱导同态的莱夫谢茨数。如果 L(�) 6 0，则每个 n 值多重映射同伦 to 都有一个不动点。如果 X 是圆，则 � 的 Lefschetz 数与单值情况下的 Schirmer 尼尔森数 N(�) 相关，即 N(�) = |L(�)|。主题分类 55M20；域中具有系数的 55N25 个同调群，他认为所有这些都诱发了 φ 的同态。当 φ 是单值连续函数时，该向量空间由通常的诱导同调同态的标量倍数组成。如果 X 是有限多面体，那么有理系数 H*(X) 的同调是有限维的，并且 h = {hk: Hk(X) → Hk(X)} 是分级同态，那么它的 Lefschetz 数 �(h) 定义为
An n-valued multimap is a continuous multivalued function �: X ⊸ Y such that �(x) is an unordered subset of n points of Y for each x ∈ X. If X and Y are finite polyhedra, theninduces a graded homomorphism of homology with rational coefficients. For�: X ⊸ X the Lefschetz number L(�) ofis defined to be the Lefschetz number of the induced homomorphism. If L(�) 6 0, then every n-valued multimap homotopic tohas a fixed point. If X is the circle, then the Lefschetz number of � is related to the Nielsen number N(�) of Schirmer as in the single-valued case, that is, N(�) = |L(�)|. Subject Classificaton 55M20; 55N25 of homology groups with coefficients in a field, all of which he c sidered induced homomorphisms of φ. When φ is a single-valued continuous function, this vector space consists of the scalar mul- tiples of the usual induced homology homomorphism. If X is a finite polyhedron, so the homology with rational coefficientsH∗(X) is finite-dimensional, and h = {hk: Hk(X) → Hk(X)} is a graded homomorphism, then its Lefschetz number �(h) is defined by