ON THE GENUS OF SMOOTH 4-MANIFOLDS

被引：11

作者：

CAVICCHIOLI, A ^{[1
]}

机构：

[1] UNIV BASILICATA,IST MATEMAT,I-85100 POTENZA,ITALY

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 331卷 / 01期

关键词：

SMOOTH; 4-MANIFOLD; CRYSTALLIZATION; GENUS; COLLAPSING; INTERSECTION FORM; HOMOTOPY SPHERE;

D O I：

10.2307/2154004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The projective complex plane and the "twisted" S3 bundle over S1 are proved to be the unique closed prime connected (smooth or PL) 4-manifolds of genus two. Then the classification of the nonorientable 4-manifolds of genus 4 is given. Finally the genus of a manifold M is shown to be related with the 2nd Betti number of M and some applications are proved in the general (resp. simply-connected) case.

引用

页码：203 / 214

页数：12

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