Manifolds in general

1-manifolds

real line vs projective line
circle from a Euclidean loop to a Lie group
curve
knot, link and Jones polynomial. Prime knots
torus knots
braid
loop and string, Witten M-Theory
fundamental group
graph and graph theory

2-manifolds

Mobius strip
surface
two sphere
torus
projective plane
Klein bottle
genus (genus of topological surface)
Euler characteristic (Euler's polyhedron formula)
Gaussian curvature
Nielsen-Thurston classification of surface homeomorphisms

3-manifolds

$\mathbb{R}^3$ Euclidean three-space
three sphere, ,
surface bundle
circle bundle, lens space, Seifert fiber space
homology sphere
Poincare conjecture
Dehn's lemma, loop theorem, sphere theorem
annulus and torus theorems
Hopf bundle

4-manifolds

Donalson's theory
quaternions
relativity, space-time
surface bundles over surfaces
spin structures
there are homeomorphic four-manifolds with differentiable structures each, which make them non-diffeomorphic.
gauge theory: monopoles
classification of simply connected 4-manifolds
intersection form
geometrization

Mathematical physics

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See Also: topology

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Cross-references: intersection, simply connected, gauge, differentiable, homeomorphic, structures, quaternions, Hopf bundle, annulus, sphere theorem, loop theorem, Dehn's lemma, Poincare conjecture, homology sphere, circle bundle, homeomorphisms, Gaussian curvature, Euler's polyhedron, Euler characteristic, genus of topological surface, genus, Klein bottle, projective plane, sphere, surface, Mobius strip, graph theory, graph, fundamental group, string, braid, torus, prime knots, polynomial, link, knot, curve, Lie group, loop, Euclidean, circle, projective line, line, real, CW complex, theory, group, piecewise, classes, characteristic, fiber bundle, cohomology, homology, homeotopy, mapping class group, isotopy, homotopy groups, homotopy, manifold, topology
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This is version 11 of topics on low dimensional topology, born on 2006-06-22, modified 2007-01-06.
Object id is 8072, canonical name is TopicsOnLowDimensionalTopology.
Accessed 1596 times total.

Classification:

AMS MSC:	57-00 (Manifolds and cell complexes :: General reference works )
	57M99 (Manifolds and cell complexes :: Low-dimensional topology :: Miscellaneous)

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