Euler characteristic interpreted by intersection theory

Abstract

We introduce definitions of Euler characteristic in intersection theory, fixed point theory, vector field theory, and Morse theory. In each theorem, Euler characteristic is defined as a sum of 'certain values' at 'certain points'. In this thesis, by studying the relations and meaning of the points and values, we can interpret the Euler characteristic with one statement: Euler characteristic is a sum of orientation numbers at nondegenerate intersections.;많은 이론들에서 정의된 Euler characteristic은 특정 점에서의 특정 값들의 합이다. 본 논문에서는 이러한 점들과 값들의 관계, 그리고, 그 의미를 연구함으로써 많은 Euler characteristic의 정의를 'nondegenerate intersection 에서의 orientation number 들의 합'으로 재해석하였다.