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de-Rham cohomology $H^1(S)$ and $ \operatorname{Hom}(\pi_1(S, s_0), (\mathbb{R},+))$ are isomorphic?

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#differential-geometry #algebraic-topology #manifolds #homology-cohomology #fundamental-groups
883
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Inclusion of path connected component induces isomorphism between fundamental groups.

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#algebraic-topology #homotopy-theory #fundamental-groups
521
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Fundamental group of space form by gluing boundary of Mobius band to $S^1 \vee S^1$

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#algebraic-topology #fundamental-groups
613
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Homotopy group of three spheres

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#algebraic-topology #homotopy-theory #fundamental-groups
212
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definition of first homology group

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#homology-cohomology #fundamental-groups
463
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Fundamental group of wedge sum of two coni over Hawaiian earrings

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#general-topology #fundamental-groups
114
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triviality of etale fundamental group vs triviality of topological fundamental group

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#algebraic-geometry #algebraic-topology #fundamental-groups #arithmetic-geometry
95
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Non-Homeomorphicity of Compact surfaces

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#algebraic-topology #group-isomorphism #fundamental-groups #compact-manifolds
777
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Fundamental group obtained by glueing two mobius bands

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#general-topology #algebraic-topology #fundamental-groups
478
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Is this space $S^3$?

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#general-topology #algebraic-topology #homology-cohomology #fundamental-groups
59
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Natural surjection that maps loops to cycles

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#riemannian-geometry #homology-cohomology #fundamental-groups #compact-manifolds
60
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Homotoping curves in 3/4-manifolds to lie on embedded tori?

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#differential-topology #geometric-topology #fundamental-groups
610
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There is no 3-dimensional manifold with fundamental group isomorphic to direct sum of four copies of $\Bbb Z$

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#algebraic-topology #fundamental-groups
70
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prove by induction that $\pi_1(\mathbb{RP}^n) = \mathbb{Z}_2$

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#algebraic-topology #fundamental-groups
472
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Does the Union of simply connected spaces with with certain conditions,simply connected?

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#general-topology #algebraic-topology #fundamental-groups #path-connected

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