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17 votes

2 answers

1k views

Homotopy equivalent but non-homeomorphic high-dimensional manifolds

asked Apr 6 at 11:39

8 votes

1 answer

281 views

Non-compact three-manifolds with the same proper homotopy type are homeomorphic?

asked Dec 16, 2022 at 6:18

7 votes

1 answer

266 views

Stallings' binding tie

asked Sep 8, 2021 at 13:28

7 votes

1 answer

240 views

If the number of ends of Freudenthal space is infinite, then its space of ends is homeomorphic to the Cantor set?

asked Dec 5, 2022 at 19:14

6 votes

0 answers

149 views

What is the minimum $n$ for which $\Bbb H^3$ can be isometrically embedded in $\Bbb R^n$ as a bounded set?

asked Jan 7, 2023 at 9:38

5 votes

1 answer

217 views

How many pairwise non-homeomorphic non-empty closed subsets of the Cantor set are there? [duplicate]

asked Nov 12, 2022 at 6:17

5 votes

0 answers

164 views

The fundamental group of the complement of badly embedded open $n$-ball in $\Bbb R^n$

asked Dec 3, 2022 at 6:03

5 votes

0 answers

131 views

Earliest known proof of "Any degree one self-map of an orientable connected finite-type non-compact surface is homotopic to a homeomorphism"

asked Sep 5, 2022 at 7:10

4 votes

2 answers

132 views

Characterization of a non-trivial non-peripheral element of the free homotopy classes of a compact bordered surface

asked Sep 21, 2022 at 12:12

4 votes

1 answer

184 views

Inequivalent free $\Bbb Z/n\Bbb Z$-actions on orientable compact bordered surface

asked Dec 11, 2021 at 12:54

4 votes

1 answer

163 views

Examples of Noetherian integral group ring

asked Mar 26 at 12:16

3 votes

1 answer

266 views

Classification of degree one map between two closed orientable surfaces without using induction on the genus

asked May 31, 2022 at 9:49

3 votes

0 answers

194 views

An almost complex structure on $\Bbb S^n$ induces a cross product on $\Bbb R^{n+1}$

asked Dec 19, 2023 at 6:25

3 votes

1 answer

117 views

A closed curve can be homotopic to remove all intersections with a filling $\Gamma$ if it has zero geometric intersection numbers with $\Gamma$

asked Sep 24, 2022 at 12:42

3 votes

0 answers

214 views

The boundary of the transversal pre-image of a submanifold with boundary

asked Mar 27, 2022 at 5:16

3 votes

1 answer

236 views

Example of a non $\pi_1$-injective, degree one, self-map of a three-manifold

asked Feb 3, 2023 at 5:36

2 votes

1 answer

177 views

Isotopic homeomorphisms of surface induces same map on the space of ends

asked May 27, 2022 at 18:47

2 votes

0 answers

106 views

Vanishing of Goldman bracket requires simple-closed representative?

asked Sep 30, 2022 at 7:02

2 votes

1 answer

295 views

In which dimensions is it true that every topological ball embedded by a smoothly embedded sphere is a smoothly embedded ball?

asked Jan 21, 2022 at 12:33

2 votes

0 answers

165 views

A property of the Riemannian metric on the symmetric space $X_\textsf{d}=\textsf{SL}(d,\Bbb R)/\textsf{SO}(d)$

asked Dec 23, 2023 at 19:25

1 vote

1 answer

147 views

Transversal pre-image of a small enough trivial tubular neighborhood contains a trivial tubular neighborhood

asked Mar 26, 2022 at 8:32

1 vote

1 answer

97 views

Derivative of the symplectomorphism evaluated at a point of the zero section of the cotangent bundle

asked Dec 13, 2023 at 12:11

Stack Exchange Network

22 Questions

Homotopy equivalent but non-homeomorphic high-dimensional manifolds

Non-compact three-manifolds with the same proper homotopy type are homeomorphic?

Stallings' binding tie

If the number of ends of Freudenthal space is infinite, then its space of ends is homeomorphic to the Cantor set?

What is the minimum $n$ for which $\Bbb H^3$ can be isometrically embedded in $\Bbb R^n$ as a bounded set?

How many pairwise non-homeomorphic non-empty closed subsets of the Cantor set are there? [duplicate]

The fundamental group of the complement of badly embedded open $n$-ball in $\Bbb R^n$

Earliest known proof of "Any degree one self-map of an orientable connected finite-type non-compact surface is homotopic to a homeomorphism"

Characterization of a non-trivial non-peripheral element of the free homotopy classes of a compact bordered surface

Inequivalent free $\Bbb Z/n\Bbb Z$-actions on orientable compact bordered surface

Examples of Noetherian integral group ring

Classification of degree one map between two closed orientable surfaces without using induction on the genus

An almost complex structure on $\Bbb S^n$ induces a cross product on $\Bbb R^{n+1}$

A closed curve can be homotopic to remove all intersections with a filling $\Gamma$ if it has zero geometric intersection numbers with $\Gamma$

The boundary of the transversal pre-image of a submanifold with boundary

Example of a non $\pi_1$-injective, degree one, self-map of a three-manifold

Isotopic homeomorphisms of surface induces same map on the space of ends

Vanishing of Goldman bracket requires simple-closed representative?

In which dimensions is it true that every topological ball embedded by a smoothly embedded sphere is a smoothly embedded ball?

A property of the Riemannian metric on the symmetric space $X_\textsf{d}=\textsf{SL}(d,\Bbb R)/\textsf{SO}(d)$

Transversal pre-image of a small enough trivial tubular neighborhood contains a trivial tubular neighborhood

Derivative of the symplectomorphism evaluated at a point of the zero section of the cotangent bundle