Euler示性数的相交数表示  

Intersecting Number Representation of Euler Number

作　　者：刘昌莲 刘登品 唐九奇 LIU Changlian;LIU Dengpin*;TANG Jiuqi(College of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《安庆师范大学学报（自然科学版）》2023年第2期27-30,共4页Journal of Anqing Normal University(Natural Science Edition)

摘　　要：Euler示性数作为拓扑学中的一个重要不变量,其涉及了组合中的Euler定理、代数拓扑中的Euler-Poincaré公式和微分拓扑中的Poincaré-Hopf指标定理。本文主要研究Euler示性数的一种几何拓扑表示,即相交数表示。一方面,设M是一个可定向的n维光滑紧流形,记Δ:M→M×M为对角嵌入,其像为N_1;另一方面,设s:M→TM为一个零截口,s (M)可嵌入M×M中,其像为N_2。本文证明了M的Euler示性数等于N_1与N_2的相交数,即χ(M)=N_1·N_2。Euler number is an important invariant in topology,and its representation involves the Euler theorem in combi-nation,the Euler-Poincaréformula in algebraic topology,and the Poincaré-Hopf index theorem in differential topology.This article studys another type of Euler number Geometric topology representation-Intersection number representation.Let M be an orientable n-dimensional smooth compact manifold,markΔ:M→M×M as diagonal embedding,and its image is N1.On the other hand,let s:M→TM be a zero-cut map.The image s(M)can be embedded in M×M,and its image is denoted as N2.We proved that the Euler number of M is equal to the number of intersections of N1 and N2,that is,χ(M)=N1⋅N2.

关 键 词：EULER数 Thom同构 Euler类 相交数 

分 类 号：O189[理学—数学]