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Covering space with transitive action is path-connected.

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#proof-verification #algebraic-topology #covering-spaces #fundamental-groups
515
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Reference request fundamental group of surface of genus $g$ and $n$ boundary components

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#algebraic-topology #surfaces #fundamental-groups #group-presentation
1k
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Correspondence between flat connections and fundamental group representations

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#differential-geometry #fundamental-groups #principal-bundles #holonomy
159
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Finite-sheeted covers of integer homology spheres

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#algebraic-topology #covering-spaces #fundamental-groups #low-dimensional-topology
100
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Path component of a topological space containing $x_0$ contains all the loops based at $x_0$.

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#proof-verification #algebraic-topology #fundamental-groups #path-connected
370
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Does any isomorphism between $\pi_1(X,x_0)$ and $\pi_1(Y,y_0)$ always induce a homeomorphism between $(X,x_0)$ and $(Y,y_0)$?

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#general-topology #algebraic-topology #group-isomorphism #fundamental-groups
98
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Fundamental group of projective plane with g handles by van Kampen

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#algebraic-topology #fundamental-groups
1.6k
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$S^1$ is not simply connected.

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#algebraic-topology #fundamental-groups #path-connected
157
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How to reconcile two different computed first homology groups for this space?

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#algebraic-topology #homology-cohomology #fundamental-groups #group-presentation
857
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Is every finitely generated group the fundamental group of some finite topological space?

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#general-topology #fundamental-groups
307
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Fundamental group about fibration

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#algebraic-topology #fundamental-groups #fiber-bundles #fibration
114
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Finding the Fundamental Group of a generic space X

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#general-topology #algebraic-topology #homotopy-theory #fundamental-groups
240
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Fundamental group of a quotient of a cylinder

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#general-topology #algebraic-topology #fundamental-groups #semidirect-product
91
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Wrong calculation of the knot group of a trefoil

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#algebraic-topology #fundamental-groups #knot-theory
160
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$\pi_1(\mathbb{R}^2\setminus (\mathbb{Z}\times 0))$

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#algebraic-topology #fundamental-groups

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