Witten's conjecture and Property P

Details Witten's conjecture and Property P Witten's conjecture and Property P

2003-11-27

arxiv.org/abs/math/0311489v5

Geom. Topol. 8(2004) 295-310

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper7.abs.html Version 5: links corrected

Scientific paper

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.

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