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Suppose that $X$ is homotopy-equivalent to a one-point space, then each point of $X$ is a deformation retract of $X$.

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#general-topology #algebraic-topology
699
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Intuition for local degree formula for singular homology map between n-spheres

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#algebraic-topology #homology-cohomology #homology-sphere
234
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$p$-localization and $p$-completion of a finite group coincide.

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#group-theory #algebraic-topology #abelian-groups
835
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Reference Request: Abelianization of free product is the direct sum of abelianizations

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#abstract-algebra #group-theory #reference-request #algebraic-topology
119
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What is the total space of the universal bundle over $B\mathbb{Q}$?

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#algebraic-topology #classifying-spaces #eilenberg-maclane-spaces
288
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Diff$(S^1)$ is deformation retracts to $O(2)$

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#analysis #algebraic-topology
687
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Singular homology - take every possible map?

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#algebraic-topology #homology-cohomology
121
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Original source of the persistence algorithm?

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#reference-request #algebraic-topology #algorithms #math-history #topological-data-analysis
53
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Double Complex with exact co-boundary operator on forms with compact support

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#algebraic-topology #differential-forms #de-rham-cohomology
61
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Computing Cohomology of $S^2/\sim$, not Hausdorff

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#algebraic-topology #homology-cohomology
208
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Transitivity of the action in definining principal bundles

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#general-topology #algebraic-topology #group-actions #principal-bundles
564
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$\mathbb CP^n$ with a quadric removed is homeomorphic to $T(\mathbb RP^n)$.

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#geometry #algebraic-topology #diffeomorphism
144
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Thom space, homotopy group and cohomology group

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#algebraic-topology #differential-topology #vector-bundles #spectral-sequences #cobordism
634
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Rank of the 2-cover space of a knot space

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#reference-request #algebraic-topology #knot-theory
230
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Rotman's proof of $H_1(X,x_0) \cong H_1(X)$

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#abstract-algebra #algebraic-topology #category-theory #proof-explanation #homological-algebra

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