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Results tagged with gt.geometric-topology
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user 65
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).
4
votes
Construction of maps $f:S^3 \to S^2$ with arbitrary Hopf invariant?
Actually, yes, there is a construction involving complex projective line.
Consider all points (x1, x2, x3, x4) on a 3-sphere in the 4-dimensional space. Our goal is to map them to $S^2$ which is th …
- 15.1k
5
votes
1
answer
320
views
Ramified covers of S^n
This question has been inspired by covering 3-torus post.
Is it true that any good (smooth, compact, oriented) $n$-manifold can be mapped to $S^n$ in such a way that the map is true covering away …
- 15.1k
14
votes
3
answers
2k
views
Spec Z analogue of Thurston program?
It's been known for a while that primes in number fields can be thought of, from an algebraic point of view, to be similar to knots in 3-manifolds. A good reference (thanks to this question) would be …
- 15.1k
4
votes
3
answers
2k
views
Homotopy groups of smooth manifolds?
For a fixed $d$, is there a relationship between the homotopy groups of smooth $d$-manifolds?
The $d=1$ case is trivial, but I already don't know how to approach $d=3$ (I should have said that th …
- 15.1k
7
votes
Questions about analogy between Spec Z and 3-manifolds
From reading the Morishita article 0904.3399 (page 24), there is a following analogue of Poincare conjecture:
Suppose that k is a number field whose ring of integers $\mathscr O_k$ is “cohomologic …
- 15.1k
3
votes
Galois groups vs. fundamental groups
You might like the following formal statement. Consider the field F with Galois group Gal. Then (finite) unramified extensions E/F are in 1-1 correspondence with (transitive) actions of Gal on (finite …
- 15.1k