THE SPHERICAL MODIFICATION ON SIMPLY-CONNECTED 4-MANIFOLD

Abstract

본 논문에서는 Simply-connected인 4차원 다양체로부터 spherical modification 에 의해 만들어지는 새로운 다양체가 주어진 다양체와 S^(2)상의 어떤 S^(2)-번들과의 connected sum 임을 증명한다.;In this paper, we would like to prove that a manifold obtained by a spherical modification from a simply-connected 4-dimensional manifold is of the from N#T(k) for some k∈Z, up to diffeomorphism, where T(k) is a S^(2)-bundle over S^(2) with degree k reduction of S^(1)-bundle.