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Hatcher Exercise (4.1.20)

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#algebraic-topology
328
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On Hatcher's proof that $H_0(X)$ is a direct sum of $\mathbb{Z}$s?

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#algebraic-topology
906
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Fundamental group: Attaching a disc to a path connected triangulable space

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#algebraic-topology #fundamental-groups #triangulation
216
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Relative singular chains basis

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#abstract-algebra #algebraic-topology #homological-algebra #free-groups
40
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If f is a path, [f] can be exposed as [f]=$[f_1][f_2]...[f_q]$?

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#algebraic-topology
101
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Is Orbit Criterion an abstract nonsense? Different induced fundamental groups.

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#algebraic-topology #covering-spaces #fundamental-groups
1.1k
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Deformation retraction onto the boundary

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#general-topology #algebraic-topology
279
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Verify $p _0 : [0,1] \mapsto S^1 , p_0(s)=(\cos(2 \pi s),\sin(2\pi s))$ is a covering map.

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#algebraic-topology #covering-spaces
1.3k
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Prove Simply Connected

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#general-topology #algebraic-topology #connectedness #fundamental-groups
986
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Show $\otimes$ and $*$ are the same operation on $\pi_1(G, x_0)$

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#algebraic-topology #topological-groups #fundamental-groups
75
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A question on discrete group

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#general-topology #algebraic-topology #operator-algebras #c-star-algebras #von-neumann-algebras
319
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Winding number of a loop

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#complex-analysis #algebraic-topology #winding-number
1.2k
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Full (or universal) group C*-algebra of discrete group $\Gamma$

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#general-topology #algebraic-topology #operator-algebras #c-star-algebras #von-neumann-algebras
284
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Working out an example of a Chern class

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#algebraic-geometry #algebraic-topology #characteristic-classes
220
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A question on left regular representation of a discrete group

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#algebraic-topology #operator-algebras #c-star-algebras #von-neumann-algebras

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