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For a given group $G$ there always exists a CW complex $X$ such that $\pi_1(X) \cong G.$

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#algebraic-topology #fundamental-groups #cw-complexes
222
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Fundamental group via Seifert Van-Kampen

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#general-topology #algebraic-topology #solution-verification #fundamental-groups
83
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Find the homotopy classes of based maps between two given spaces.

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#algebraic-topology #homotopy-theory #covering-spaces #fundamental-groups
96
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fundamental group for different path component

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#general-topology #algebraic-topology #fundamental-groups
134
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Homotopy groups of projective Lie groups PO(N), PSO(N), and PSpin(N)

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#lie-groups #homotopy-theory #quotient-spaces #fundamental-groups #higher-homotopy-groups
83
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The Natural Action of the Fundamental Group $\pi_1(M,p_0)$ on the Universal Covering $\widetilde{M}$

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#algebraic-topology #manifolds #group-actions #covering-spaces #fundamental-groups
161
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Covering space that corresponds to intersection of fundamental groups

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#algebraic-topology #covering-spaces #fundamental-groups
123
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Intuition behind the fundamental group $\pi_1(S^1)$

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#general-topology #geometry #algebraic-topology #homotopy-theory #fundamental-groups
123
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Elementary proof that the Griffiths twin cone is not simply connected

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#general-topology #homotopy-theory #fundamental-groups
112
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Simplicial complex with prescribed fundamental group

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#algebraic-topology #fundamental-groups #simplicial-complex
955
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Fundamental group of $n$-punctured torus

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#algebraic-topology #fundamental-groups
290
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Fundamental group of a compact surface

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#surfaces #fundamental-groups
224
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why they have the same first coordinate in torus?

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#algebraic-topology #fundamental-groups
109
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Generators of $\pi_1(\mathbb{RP}^n)$

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#algebraic-topology #homology-cohomology #fundamental-groups #projective-space #spheres
220
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Detect a knot from its fundamental group

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#fundamental-groups #knot-theory #braid-groups

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