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Results tagged with gt.geometric-topology
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user 61824
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
1
answer
227
views
Example similar to the Griffiths twin cone but with fundamental group that allows surjection...
The Griffiths twin cone is an example of a wedge sum of two contractible spaces being non-contractible. Namely, it is the wedge sum $\mathbb G=C\mathbb H\vee_p C\mathbb H$ of two coni over the Hawaiia …
6
votes
1
answer
360
views
Immersion in $\mathbb R^3$ of a Klein bottle with Morse-Bott height function without centers
Can the Klein bottle be immersed in $\mathbb R^3$ so that the associated height function be of Morse-Bott type and have no centers?
That is, the height function would have only Bott-type extrema and …
4
votes
1
answer
490
views
Immersion of non-orientable surface in $\mathbb R^3$ with conditions on the height function
EDIT: The answer is trivially positive; the question arose from my misunderstanding of the figure below.
Can a non-orientable closed surface of odd genus be immersed in $\mathbb R^3$ so that the assoc …