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topics on low dimensional topology
List of topic on low dimensional topology that should be here at PM
1 Manifolds in general
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homology and cohomology
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piecewise linear topology
2 1-manifolds
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knot, link and Jones polynomial. Prime knots
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torus knots
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loop and string, Witten M-Theory
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graph and graph theory
3 2-manifolds
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two sphere
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torus
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Nielsen-Thurston classification of surface homeomorphisms
4 3-manifolds
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Euclidean three-space
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three sphere, ,
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surface bundle
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circle bundle, lens space, Seifert fiber space
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Dehn’s lemma, loop theorem, sphere theorem
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annulus and torus theorems
5 4-manifolds
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Donalson’s theory
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relativity, space-time
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surface bundles over surfaces
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spin structures
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there are homeomorphic four-manifolds with differentiable structures each, which make them non-diffeomorphic.
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gauge theory: monopoles
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classification of simply connected 4-manifolds
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intersection form
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geometrization
6 Mathematical physics
Mathematics Subject Classification
57M99 None of the above, but in MSC2010 section 57Mxx57-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
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