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Map $\langle X, Y\rangle \to \text{Hom}(\pi_n(X), \pi_n(Y))$ bijection?

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#algebraic-topology #category-theory #homological-algebra #homology-cohomology #homotopy-theory
57
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When is the equivalence class of a continuous map $f: S^n \to X$ such that $[f]=1\in \pi_n(X)$?

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#reference-request #algebraic-topology #homotopy-theory
551
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Homotopic to a constant map $f$ and the $f_{\#}$

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#algebraic-topology #homotopy-theory
485
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Is delooping of a topological space unique up to homotopy equivalence?

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#algebraic-topology #homotopy-theory #loop-spaces
118
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cofinal subsequence is homotopy cofinal

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#reference-request #algebraic-topology #homotopy-theory
149
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How to compare the group operations in homotopy and homology groups?

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#reference-request #algebraic-topology #homology-cohomology #homotopy-theory
112
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Is there an analog of the Thom-Pontryagin construction for manifolds besides spheres?

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#reference-request #differential-topology #intuition #homology-cohomology #homotopy-theory
569
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Uniqueness of Moore Spaces

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#algebraic-topology #homotopy-theory
264
Views

cellular homology/triangulations of suspensions, mapping cones and cylinders

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#reference-request #algebraic-topology #homological-algebra #homotopy-theory #book-recommendation
510
Views

Fundamental Group of a Quotient of an Annulus

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#algebraic-topology #homotopy-theory #fundamental-groups
50
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Why is $\pi_3(S^2\cup_f e^4)=\mathbb{Z}_5$?

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#algebraic-topology #homotopy-theory
832
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Tangent bundle and manifold are homotopy equivalent

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#differential-geometry #homotopy-theory #fundamental-groups
93
Views

Understanding Hatcher's corollary 4.25

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#algebraic-topology #homology-cohomology #homotopy-theory
188
Views

Every class in $H_{n - 1}(M; \mathbb{Z})$ represented by closed, smooth, orientable submanifold of codimension $1$?

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#algebraic-topology #manifolds #homology-cohomology #homotopy-theory
144
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Homotopy classes of maps from $S^1$ to the Grassmanian $G_n(\mathbb{R}^{\infty})$

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#algebraic-topology #homotopy-theory #vector-bundles #grassmannian

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