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Results tagged with at.algebraic-topology
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user 17029
Homotopy theory, homological algebra, algebraic treatments of manifolds.
14
votes
Accepted
Existence of a non-null-homotopic simple closed curve
No. The harmonic archipelago is a compact $2$-dimensional counterexample, embedded in $\mathbb R^3$.
Let $S_n$ denote the planar circle with center on the $x$-axis, and whose intersection with the $x …
- 1,968
11
votes
Are the higher homotopy groups of the Hawaiian earring trivial?
Here is a short natural argument that planar continua are aspherical, different from the technique of Cannon/Conner/Zastrow, and straight forwardly applied to the Hawaiian earring.
The Hawaiian earr …
- 1,968
10
votes
Accepted
Is the homeomorphism class of a connected open set of C determined by its fundamental group?
The answer is indeed no as David Cohen has pointed out, and more generally the answer is determined by the complements of the sets U and U'.
The complete solution is effectively due to R.L. Moore (19 …
- 1,968
3
votes
Homotopy problem for infinite dimensional topological space II
The following does not settle the original question.
The answer is `no' if we ignore the intrinsic metric requirement and merely demand metric.
For a counterexample first observe that the inverse li …
- 1,968
2
votes
0
answers
131
views
Topological dimension of quotient group determined by the inverse limit of discrete free mon...
Must the natural quotient group of the inverse limit of a sequence of nested discrete free monoids have topological dimension zero?
The question might well be open, but I would be grateful for news t …
- 1,968