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Is this inclusion a cofibration?

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#general-topology #algebraic-topology #obstruction-theory
68
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Commutativity of fibrations up to homotopy implies commutativity

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#general-topology #algebraic-topology #homotopy-theory
72
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If $f_0=\omega_m$ and $f_1=\omega_n$, why is it not automatic that $\tilde f_0 = \tilde \omega_m$ and $\tilde f_1 = \tilde \omega_n$?

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#group-theory #algebraic-topology #proof-explanation #covering-spaces #fundamental-groups
2.8k
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What needs to be done to prove that a vector bundle is trivial?

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#algebraic-topology
161
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Spaces of submanifolds

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#differential-geometry #algebraic-topology #differential-topology #smooth-manifolds
556
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Show that a closed path is homotopic to a constant path

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#general-topology #algebraic-topology
819
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Loops as maps from $S^1\to X$, Hatcher 1.15

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#algebraic-topology #homotopy-theory #fundamental-groups
47
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Operation with graphs

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#graph-theory #algebraic-topology
79
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How does Hatcher conclude that the set of points where $\tilde f_1$ and $\tilde f_2$ agree is both open and closed?

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#proof-verification #algebraic-topology #proof-explanation
609
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Is a closed embedding of CW-complexes a cofibration?

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#general-topology #algebraic-topology #cw-complexes #cofibrations
308
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Canonical section of a Hirzebruch surface

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#algebraic-geometry #algebraic-topology #complex-geometry #holomorphic-bundles
71
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Embedding Dimension of a graph

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#general-topology #graph-theory #algebraic-topology
97
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Topology on the space of functions

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#general-topology #functional-analysis #algebraic-topology #metric-spaces
72
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First fundamental group and connectedness of $X:=\mathbb{R^4}\setminus \{\pi_1 \cup \pi_2 \}$

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#general-topology #algebraic-topology #fundamental-groups
219
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Does the triviality of the orthonormal frame bundle imply the triviality of the spin bundle?

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#algebraic-topology #spin-geometry

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