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how many circles is a connected graph homotopically equivalent to?

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#algebraic-topology #homotopy-theory
88
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Homeomorphism between a subset of $S^n \times S^n$ and a hemisphere times $S^{n-1}$?

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#algebraic-topology #homology-cohomology #homotopy-theory #geometric-topology
1k
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Concretely, what is the horn $\Lambda_k^n$?

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#algebraic-topology #category-theory #homotopy-theory
556
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Fundamental group of mapping torus of $\mathbb{R}P^2 \vee \mathbb{R}P^2$

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#general-topology #algebraic-topology #homotopy-theory #fundamental-groups
60
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Induced map on homology of $\mathbb{R}P^n \vee \mathbb{R}P^n$ from interchanging copies of $\mathbb{R}P^n$

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#general-topology #algebraic-topology #homology-cohomology #homotopy-theory
82
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Induced map on homology of $\mathbb{C}P^n$ by exchanging coordinates

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#general-topology #algebraic-topology #homology-cohomology #homotopy-theory
41
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A Homotopy equivalence between two sets($A$ and $S^1$)

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#general-topology #algebraic-topology #homotopy-theory
371
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Equivalence homotopy between $\Bbb R^2$\-{$(0,0)$} and a convex set without a point

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#general-topology #algebraic-topology #homotopy-theory
137
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$\pi_2(X)$ defined with closed surfaces instead of spheres

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#reference-request #algebraic-topology #homotopy-theory
379
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Classifying space of a group

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#group-theory #algebraic-topology #homotopy-theory #fiber-bundles #classifying-spaces
165
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Usage of sending curve from fundamental group to the endpoint of its lift?

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#algebraic-topology #homotopy-theory #fundamental-groups
611
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How to explicitly perform the circle eversion in the $3$-dimensional space?

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#differential-geometry #circles #homotopy-theory #orientation
2.9k
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Universal covering spaces of homotopy equivalent spaces are homotopy equivalent

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#algebraic-topology #homotopy-theory #covering-spaces
36
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Homotopies in the Moebius strip

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#algebraic-topology #homotopy-theory
1.2k
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About the second homotopy group of a Lie group

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#lie-groups #homotopy-theory

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