2003/11/30 by P B Kronheimer, T S Mrowka · 1 citation
Mathematics · #math.GT #msc:57M25 #msc:57R57 #msc:57R17
paper · pdf · doi:10.2140/gt.2004.8.295
published as Geom. Topol. 8 (2004) 295-310 · Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper7.abs.html Version 5: links corrected
arxiv created 2004/02/22 · arxiv updated 2014/11/11
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.