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Example of non-homotopic functions

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#homotopy-theory
55
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Prove sequence has limit in $\gamma (S^1)$

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#sequences-and-series #algebraic-topology #homotopy-theory
218
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extending maps from spaces to their whitehead towers

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#algebraic-topology #homotopy-theory #fiber-bundles #principal-bundles #fibration
91
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Why the Objects of Homotopy Category not Homotopy Classes of Spaces?

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#algebraic-topology #homotopy-theory
129
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Use Hurewicz Theorem to calculate $\pi_3(\mathbb{R}P^4 \vee S^3)$

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#algebraic-topology #homotopy-theory
107
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Generalisation of Adams spectral sequence to triangulated categories

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#algebraic-topology #homotopy-theory #spectral-sequences #triangulated-categories
101
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Stack on commutative ring spectra?

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#homotopy-theory #algebraic-stacks
1.3k
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Showing $S^1$ is not a retract of $D^2$ using homotopy

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#algebraic-topology #homotopy-theory
738
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How to construct a quasi-category from a category with weak equivalences?

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#category-theory #homotopy-theory #simplicial-stuff #higher-category-theory
2.1k
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Show $f$ has a fixed point if $f\simeq c$

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#algebraic-topology #homotopy-theory #winding-number
251
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How to Kill Homotopy Groups Using Framed Cobordism?

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#reference-request #algebraic-topology #manifolds #differential-topology #homotopy-theory
249
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morphisms of principal bundles with different structure groups

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#algebraic-topology #homotopy-theory #principal-bundles #fibration
467
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Cofiber Sequences in Reduced Homology Theory

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#algebraic-topology #homotopy-theory #homology-cohomology
819
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The unit ball in $\mathbb{R}^{n}$ and a point are homotopically equivalent.

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#general-topology #homotopy-theory
851
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In the definition of $n$-equivalence, what is the motivation for only requiring surjectivity on the $n$th dimension.

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#algebraic-topology #homotopy-theory

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