List questions from geometric-topology

Published on 25 Feb 2021 - 23:18

67

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Let $O_1$, $O_2\subset \mathbb{R}^3$ be two open sets and $\phi:O_1\rightarrow O_2$ a diffeomorphism.

Published on 26 Feb 2021 - 1:56

152

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How to "topologically neutralize" this curious manifold?

Published on 26 Mar 2026 - 22:58

167

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Lift of a shortest loop is length minimizing

Published on 26 Feb 2021 - 6:06

77

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Pathological Examples in Smash Products?

Published on 06 Apr 2026 - 0:40

196

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Is it always possible to extend a homeomorphism from a closed ball in the plane onto a closed disk in a surface to their neighbourhoods?

Published on 25 Mar 2026 - 23:42

119

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Homeomorphism of the plane that takes a simple closed curve to a circle and is the identity off of a compact set

Published on 02 Mar 2021 - 6:36

64

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Some confuse in spectral sequence and its calculate

Published on 26 Mar 2026 - 20:44

640

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How do I show that a domain is not simply connected?

Published on 02 Mar 2021 - 10:54

94

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If $f:S\rightarrow \mathbb{R}^m$ is a map such that each $f|_{S_i}:S_i\rightarrow \mathbb{R}^m$ is differentiable, prove that $f$ is differentiable.

Published on 03 Mar 2021 - 0:22

107

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What is the optimal dimension $k$ for which $S^2\times S^2$ into $\mathbb{R}^k$?

Published on 03 Mar 2021 - 9:09

29

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Discrete arithmetic subgroup

Published on 03 Mar 2021 - 10:52

135

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Writing down homeomorphisms in a formula

Published on 07 Mar 2021 - 8:17

90

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Genus of a Canonical Product v.s. Genus of a Torus

Published on 09 Mar 2021 - 7:00

622

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Prime 3-Manifolds

Published on 10 Mar 2021 - 8:44

List Question

Relation between the topology definition and the real example

Let $O_1$, $O_2\subset \mathbb{R}^3$ be two open sets and $\phi:O_1\rightarrow O_2$ a diffeomorphism.

How to "topologically neutralize" this curious manifold?

Lift of a shortest loop is length minimizing

Pathological Examples in Smash Products?

Is it always possible to extend a homeomorphism from a closed ball in the plane onto a closed disk in a surface to their neighbourhoods?

Homeomorphism of the plane that takes a simple closed curve to a circle and is the identity off of a compact set

Some confuse in spectral sequence and its calculate

How do I show that a domain is not simply connected?

If $f:S\rightarrow \mathbb{R}^m$ is a map such that each $f|_{S_i}:S_i\rightarrow \mathbb{R}^m$ is differentiable, prove that $f$ is differentiable.

What is the optimal dimension $k$ for which $S^2\times S^2$ into $\mathbb{R}^k$?

Discrete arithmetic subgroup

Writing down homeomorphisms in a formula

Genus of a Canonical Product v.s. Genus of a Torus

Prime 3-Manifolds

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