Witten's conjecture and property P

被引：66

作者：

Kronheimer, PB ^{[1
]}

Mrowka, TS

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

GEOMETRY & TOPOLOGY | 2004年 / 8卷

基金：

美国国家科学基金会;

关键词：

3-manifold; knot; surgery; homotopy sphere; gauge theory;

D O I：

10.2140/gt.2004.8.295

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a non-trivial knot in the 3-sphere and let Y be the 3-manifold obtained by surgery on K with surgery-coefficient 1. Using tools from gauge theory and symplectic topology, it is shown that the fundamental group of Y admits a non-trivial homomorphism to the group SO(3). In particular, Y cannot be a homotopy-sphere.

引用

页码：295 / 310

页数：16

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