乘积流形的曲面和与流形亏格的可加性

Surface sum of product manifolds and the additivity of genus of manifolds

设M=(P1×I)∪F(P2×I),其中F是P1×{0}和P2×{0}上的连通的带边不可压缩曲面,P1和P2都是正亏格的连通的可定向的闭曲面.重点研究g(M)与g(P1),g(P2)以及g(F)的关系,不仅给出了一些具体的估计,并且证明了当F满足某些条件时g(M)=g(P1)+g(P2)成立,从而得出了乘积流形的曲面和具有亏格可加性.

Let M=（P1×I）∪ F（P2×I）,where F is a connected bounded incompressible surface on both P1×{0} and P2×{0},P1 and P2 are connected orientable closed surfaces with genus at least one.In this paper we mainly consider the relation between g（M）,g（P1）,g（P2）and g（F）,we not only give the estimation of the genus of g（M） but also prove that the genus of product manifolds are additive under surface sum if the attaching surface F satisfy certain conditions.