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그로모브-위튼 불변량과 그의 응용

  • 조용승 (이화여자대학교 자연과학대학 수학과)
  • Published : 2004.07.01

Abstract

심프렉틱 다양체는 미분다양체와 케러다양체 사이에 있는 다양체로서 심프렉틱 구조를 갖는 다양체이다. 케러다양체의 성질들을 얼마나 확장할수 있는지, 미분다양체와 다른 성질은 무엇이 있는지 연구함은 흥미있는 일이다. 심프렉틱 구조로부터 준복소구조가 정의되어 2차원 부분다양체를 나타내는 슈도-호로모르픽 사상이 정의되고, 이들은 모듀라이 공간이 된다. 또한 심프렉틱 구조는 메트릭과 에너지를 정의하여 노비코프환을 정의한다. 여기서 모듀라이 공간의 위상구조가 그로모브-위튼 불변량을 정의한다. 이 불변량은 심프렉틱 다양체 연구에 핵심적인 역할을 한다. 이 논문은 그로모브-위튼 불변량의 여러 가지 성질과 그 응용에 대한 여러 학자들의 결과를 소개하는 해설 논문이다.

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