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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manifold^{}

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homotopy^{}, homotopy groups^{},

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isotopy^{}, mapping class group^{}, homeotopy

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homology^{} and cohomology^{}
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piecewise linear topology

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topological methods in group theory
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2 1manifolds
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curve

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knot, link and Jones polynomial^{}. Prime knots^{}
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braid

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loop and string, Witten MTheory
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graph and graph theory^{}
3 2manifolds
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two sphere

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torus
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genus (genus of topological surface)

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Euler characteristic^{} (Euler’s polyhedron formula)
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NielsenThurston classification of surface homeomorphisms^{}
4 3manifolds

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${\mathbb{R}}^{3}$ Euclidean threespace

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${S}^{3}$ three sphere, $SO(3)$, $SU(2)$

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surface bundle

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circle bundle^{}, lens space, Seifert fiber space (http://planetmath.org/SeifertFiberSpace)
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Dehn’s lemma, loop theorem, sphere theorem

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annulus^{} and torus theorems
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5 4manifolds

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Donalson’s theory

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quaternions

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relativity, spacetime

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surface bundles over surfaces

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spin structures

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there are homeomorphic fourmanifolds with differentiable structures each, which make them nondiffeomorphic.

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gauge theory: monopoles

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classification of simply connected 4manifolds

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intersection form

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geometrization
6 Mathematical physics
Title  topics on low dimensional topology 

Canonical name  TopicsOnLowDimensionalTopology 
Date of creation  20130322 16:01:46 
Last modified on  20130322 16:01:46 
Owner  juanman (12619) 
Last modified by  juanman (12619) 
Numerical id  14 
Author  juanman (12619) 
Entry type  Topic 
Classification  msc 57M99 
Classification  msc 5700 
Related topic  Topology^{} 