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how to prove this homotopic problem

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#homotopy-theory #winding-number
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Are $[0,1]$ and $(0,1)$ homotopy equivalent?

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#algebraic-topology #homotopy-theory #alternative-proof
282
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two maps are not homotopic equivalent

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#algebraic-topology #homological-algebra #homotopy-theory
90
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the quotien space of $ S^1\times S^1$

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#general-topology #algebraic-topology #homology-cohomology #homotopy-theory
63
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Can $X=SO(n)\setminus\{I_n\}$be homeomorphic to or homotopic equivalent to product of spheres?

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#general-topology #algebraic-topology #homology-cohomology #homotopy-theory
125
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Why do $S^1 \wedge - $ and $Maps(S^1,-)$ form a Quillen adjunction?

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#algebraic-topology #homotopy-theory #model-categories
590
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Is $S^{n-1}$ a deformation retract of $S^{n}$ \ {$k$ points}?

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#algebraic-topology #homotopy-theory
523
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Connection between Mayer-Vietoris and higher dimensional Seifert-Van Kampen Theorems

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#algebraic-topology #soft-question #homological-algebra #homotopy-theory
162
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Why is the number of exotic spheres equivalent to $S^7,S^{11},S^{15},S^{27}$ equal to perfect numbers?

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#algebraic-topology #differential-topology #homotopy-theory
99
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Are the maps homotopic?

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#general-topology #homotopy-theory
443
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Is loop spaces are homotopy equivalent

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#algebraic-topology #homotopy-theory
104
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Showing that a path is a non-trivial element of a fundamental group.

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#general-topology #algebraic-topology #homotopy-theory
61
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Homotopic maps between pointed sets induce same group homomorphism

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#proof-verification #homotopy-theory #fundamental-groups
272
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In what sense are (co)fibrant replacements "better"?

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#homotopy-theory #model-categories
124
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Sphere eversion in $\mathbb R^4$

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#geometry #differential-geometry #homotopy-theory #spheres #orientation

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