Contractible noncompact 3-manifold without boundary not homeomorphic to \$\Bbb R^3\$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T03:39:30Z http://mathoverflow.net/feeds/question/81811 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81811/contractible-noncompact-3-manifold-without-boundary-not-homeomorphic-to-bbb-r3 Contractible noncompact 3-manifold without boundary not homeomorphic to \$\Bbb R^3\$ lethe 2011-11-24T15:19:11Z 2011-11-25T01:18:48Z <p>I heard this example was given in Whitehead's paper A CERTAIN OPEN MANIFOLD WHOSE GROUP IS UNITY.( <a href="http://qjmath.oxfordjournals.org/content/os-6/1/268.full.pdf" rel="nofollow">http://qjmath.oxfordjournals.org/content/os-6/1/268.full.pdf</a> ) But I was confused by his term. Thus I'm looking for an explanation in more standard terms about this example.</p> <p>But since my aim is to know about an example of this kind, any alternative will do either.</p> http://mathoverflow.net/questions/81811/contractible-noncompact-3-manifold-without-boundary-not-homeomorphic-to-bbb-r3/81813#81813 Answer by Marco Golla for Contractible noncompact 3-manifold without boundary not homeomorphic to \$\Bbb R^3\$ Marco Golla 2011-11-24T15:35:47Z 2011-11-24T15:35:47Z <p>It's discussed in Kirby's "The topology of 4-manifolds", around page 80, and at a glance the argument looks "modern".</p> http://mathoverflow.net/questions/81811/contractible-noncompact-3-manifold-without-boundary-not-homeomorphic-to-bbb-r3/81814#81814 Answer by Richard Kent for Contractible noncompact 3-manifold without boundary not homeomorphic to \$\Bbb R^3\$ Richard Kent 2011-11-24T15:40:57Z 2011-11-24T15:40:57Z <p>The manifold is the <a href="http://en.wikipedia.org/wiki/Whitehead_manifold" rel="nofollow">Whitehead manifold</a>.</p>