Witten’s conjecture and Property P

Kronheimer, Peter B¹ ; Mrowka, Tomasz S²

¹ Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA
² Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Geometry & topology, Tome 8 (2004) no. 1, pp. 295-310.

Résumé

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 $SO\left(3\right)$. In particular, $Y$ cannot be a homotopy-sphere.

Détail

DOI : 10.2140/gt.2004.8.295

Keywords: 3–manifold, knot, surgery, homotopy sphere, gauge theory

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