Question

How do I prove that the union of two simply connected open sets whose intersection is path connected is simply connected?

score 3.2k · Answer 1 · 2026-04-11 04:53:04

How do I prove that the union of two simply connected open sets whose intersection is path connected is simply connected?

score 869 · Answer 2 · 2026-04-09 04:21:09

869

Views

Is the plane minus the integer lattice homeomorphic to the plane minus the integers?

Published on 09 Apr 2026 - 4:21

score 115 · Answer 3 · 2026-04-13 01:19:45

115

Views

is there a notation to designate the induced homomorphism including base point?

Published on 13 Apr 2026 - 1:19

score 687 · Answer 4 · 2026-04-10 03:32:41

687

Views

Functoriality of fundamental group

Published on 10 Apr 2026 - 3:32

score 434 · Answer 5 · 2026-04-13 20:49:41

434

Views

Pathwise, simple connectedness of real Grassmannian $G(2, 4)$

Published on 13 Apr 2026 - 20:49

score 349 · Answer 6 · 2026-04-14 02:13:37

349

Views

equivalent characterisation of simply connect spaces

Published on 14 Apr 2026 - 2:13

score 133 · Answer 7 · 2026-04-17 06:57:45

133

Views

Is there no continuous $f:\mathbb{R}^{2^{*}}\rightarrow S^1$?

Published on 17 Apr 2026 - 6:57

score 1.5k · Answer 8 · 2026-04-12 14:26:01

1.5k

Views

When is the free loop space simply connected?

Published on 12 Apr 2026 - 14:26

score 337 · Answer 9 · 2026-04-23 02:03:20

337

Views

Calculating $\pi_2$ of a certain free loop space

Published on 23 Apr 2026 - 2:03

score 32 · Answer 10 · 2026-04-14 22:06:05

32

Views

Homotopy classes of self-maps on L(2,1)#L(3,1)

Published on 14 Apr 2026 - 22:06

score 386 · Answer 11 · 2026-04-14 03:46:26

386

Views

Explicitly building Top. space with trivial homology group and non trivial fundamental group, w/o CW-complexes

Published on 14 Apr 2026 - 3:46

score 226 · Answer 12 · 2026-04-14 10:42:27

226

Views

if $\pi_1(G)$ is trivial, how to prove $ \pi_1(G/H)=\pi_0(H)/\pi_0(G) $?

Published on 14 Apr 2026 - 10:42

score 147 · Answer 13 · 2026-04-17 06:24:09

147

Views

Fibrations lift p-connectedness

Published on 17 Apr 2026 - 6:24

score 366 · Answer 14 · 2026-04-13 08:53:04

366

Views

How to show that a homomorphism between fundamental groups is an inner automorphism?

Published on 13 Apr 2026 - 8:53

score 105 · Answer 15 · 2026-04-11 00:58:19

105

Views

Definition question in algebraic topology.

Published on 11 Apr 2026 - 0:58

List Question

How do I prove that the union of two simply connected open sets whose intersection is path connected is simply connected?

Is the plane minus the integer lattice homeomorphic to the plane minus the integers?

is there a notation to designate the induced homomorphism including base point?

Functoriality of fundamental group

Pathwise, simple connectedness of real Grassmannian $G(2, 4)$

equivalent characterisation of simply connect spaces

Is there no continuous $f:\mathbb{R}^{2^{*}}\rightarrow S^1$?

When is the free loop space simply connected?

Calculating $\pi_2$ of a certain free loop space

Homotopy classes of self-maps on L(2,1)#L(3,1)

Explicitly building Top. space with trivial homology group and non trivial fundamental group, w/o CW-complexes

if $\pi_1(G)$ is trivial, how to prove $ \pi_1(G/H)=\pi_0(H)/\pi_0(G) $?

Fibrations lift p-connectedness

How to show that a homomorphism between fundamental groups is an inner automorphism?

Definition question in algebraic topology.

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