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Results tagged with gt.geometric-topology
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user 2039
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
6
votes
Accepted
Learning roadmap for geometric topology
One of the best introductions to the subject is certainly Thurston's Three-dimensional Topology and Geometry, Vol.1 (not to be confused with his much harder lecture notes Three-dimensional Topology an …
- 12.1k
8
votes
Homotopy groups other than $\pi_1$ : what are they good for?
I think, they have an intrinsic appeal: If one cares about manifolds, one should care about maps between manifolds. As maps between spaces appear so often in topology, of course also homotopy groups d …
16
votes
Accepted
Closed 3-manifolds with free abelian fundamental groups
(I assume all occuring 3-manifolds to be orientable and closed)
A manifold with a free abelian fundamental group cannot be a connected sum of non-trivial 3-manifolds since its fundamental group is no …
- 12.1k