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Does the Hairy Ball theorem imply the Borsuk-Ulam for even dimensions?

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#proof-verification #algebraic-topology #vector-fields
440
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Integral class mod 2 reduction, and Stiefel Whitney class

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#algebraic-topology #differential-topology #homology-cohomology #geometric-topology #characteristic-classes
175
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Boundaries of manifolds and algebraic topology

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#algebraic-topology #homology-cohomology #manifolds-with-boundary
66
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critical points relevant to the lowest order non-perturbative correction

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#algebraic-geometry #algebraic-topology #asymptotics #morse-theory
80
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Integral cohomology class associated to trefoil knots

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#algebraic-topology #differential-topology #homology-cohomology #geometric-topology #knot-theory
96
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Is this space simply connected?

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#algebraic-topology
505
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Different ways of identifying the boundaries of a disc with two holes

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#general-topology #algebraic-topology
103
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Decomposition of odd-dimensional oriented vector bundles

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#algebraic-topology #homotopy-theory
266
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Quotient topology and continuity

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#general-topology #analysis #algebraic-topology
282
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Oriented vs. Ordered Simplicial Homology

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#abstract-algebra #algebraic-topology #category-theory #homology-cohomology
178
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Why are some maps cofibrations

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#algebraic-topology
1.9k
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Show that if $Y$ is path-connected, then the set $[I, Y]$ (the homotopy classes of maps from $I$ to $Y$) has a single element

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#general-topology #algebraic-topology
397
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How does $\mathbb R^n\setminus \{0\}$ being simply connected follow as a corollary from $\mathbb S^{n-1}$ being a strong deformation retract?

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#general-topology #algebraic-topology #proof-explanation #homotopy-theory
213
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What is the mistake in the following cohomology computation?

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#algebraic-topology #homology-cohomology
305
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Can there be a manifold with uncountable genus? Can they be compact?

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#differential-geometry #algebraic-topology #manifolds #infinity

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