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Results tagged with gt.geometric-topology
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user 5499
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).
22
votes
1
answer
637
views
Presenting 3-manifolds by planar graphs
From a planar graph $\Gamma$, equipped with an integer-valued weight function $d:E(\Gamma) \sqcup V(\Gamma) \to \mathbb{Z}$, one can build a $3$-manifold $M_{\Gamma}$ as follows. For each vertex $v$, …
- 932
10
votes
1
answer
633
views
Self-homomorphisms of surface groups
Let $X$ be a closed, orientable surface of genus at least 2, and let $\phi: \pi_1(X) \to \pi_1(X)$ be a surjective homomorphism. Is $\phi$ necessarily injective?
- 932
5
votes
Möbius and projective 3-manifolds
If true, such a statement would immediately imply the Poincare conjecture. Indeed, suppose X were a closed, simply connected 3-manifold with a Mobius structure. Near any point of $X$, there would th …
- 932