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Constructing Finite Separable Field Extensions From Sets Equipped With a Continuous Galois Group Action

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#abstract-algebra #field-theory #galois-theory #extension-field #fundamental-groups
1.2k
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Fundamental group of $R^3$ minus two disjoint circles

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#algebraic-topology #fundamental-groups
51
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Is $[0, 1) \times (0, 1] \to D \setminus \{ 0 \}$, $(\varphi, r) \mapsto r e^{2 \pi i \varphi}$ not a homeomorphism?

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#general-topology #algebraic-topology #continuity #fundamental-groups
533
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Why are circles of opposite directions not homotopic to each other?

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#algebraic-topology #homotopy-theory #fundamental-groups
135
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How do I compute this monodromy action on the cohomology of an elliptic curve explicitly?

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#complex-analysis #homology-cohomology #elliptic-curves #fundamental-groups
56
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Categorical expresssion of the isomorphism between fundamental groups

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#algebraic-topology #category-theory #fundamental-groups
74
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Group isomorphism between identity morphisms of fundamental groupoid and fundamental group of topological space

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#category-theory #homotopy-theory #group-homomorphism #fundamental-groups #groupoids
443
Views

Fundamental group of the torus from hexagon with opposite sides identified

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#group-theory #algebraic-topology #fundamental-groups #group-presentation
212
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How to show that explicit generator of the fundamental group is the one I found?

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#general-topology #algebraic-topology #fundamental-groups #spheres
204
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A quotient space of a closed annulus is homeomorphic to a Klein bottle

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#general-topology #algebraic-topology #fundamental-groups #klein-bottle
120
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Free group of rank-$2$ has no non-trivial abelian normal subgroup

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#algebraic-topology #solution-verification #trees #covering-spaces #fundamental-groups
130
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Homotopy classes of a subset of $\mathbb{R}^2$ with two holes.

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#algebraic-topology #solution-verification #homotopy-theory #fundamental-groups
217
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Finding the image for the fundamental group of a covering of $S^1 \vee S^1$

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#algebraic-topology #covering-spaces #fundamental-groups
52
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Induced Homomorphism in the unit circle

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#algebraic-topology #cyclic-groups #group-homomorphism #fundamental-groups
142
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Realization of subgroups of $\pi_1(M)$ by submanifolds

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#algebraic-topology #manifolds #differential-topology #fundamental-groups #low-dimensional-topology

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