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Integral homology isomorphism induces an isomoprhism on weak homotopy classes of maps into a group like space

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#algebraic-topology #homotopy-theory #obstruction-theory
18
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Conditions for a lift of an arbitrary map to exist along an arbitrary map

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#general-topology #homology-cohomology #obstruction-theory
4.1k
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A complex line bundle is trivial if and only if the first Chern class is zero

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#algebraic-topology #vector-bundles #geometric-topology #characteristic-classes #obstruction-theory
288
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a question on oriented bundles and Euler class

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#algebraic-topology #vector-bundles #geometric-topology #characteristic-classes #obstruction-theory
391
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Obstruction theory for homotopies

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#algebraic-topology #homotopy-theory #obstruction-theory
118
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Nontrivial obstruction cocycle whose class is trivial

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#general-topology #algebraic-topology #obstruction-theory
487
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Obstruction Theory: extending a map on CW complexes

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#algebraic-topology #obstruction-theory
437
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Vector bundle of dimension $\leqslant n$ on $n$-connected space is trivial

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#algebraic-topology #vector-bundles #obstruction-theory
238
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Well-definedness of first obstruction (to extending a map or homotopy of maps over the skeleta of a CW complex) lying in a nonzero group

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#algebraic-topology #homotopy-theory #obstruction-theory
130
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spin structures on knot complements

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#algebraic-topology #hyperbolic-geometry #obstruction-theory
271
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Obstruction for extending a map along a CW-inclusion: sufficient conditions?

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#algebraic-topology #homotopy-theory #obstruction-theory
794
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Local coefficients involved in the obstruction class for a lift of a map

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#algebraic-topology #fibration #obstruction-theory
166
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Trivialised sub-bundle of a trivialised bundle and its orthogonal bundle

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#algebraic-topology #vector-bundles #obstruction-theory
126
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Showing that the Mobius strip is non-orientable using obstruction theory

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#algebraic-topology #obstruction-theory
1.5k
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Showing that the Hopf fibration is a non-trivial fibre bundle

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#differential-geometry #fiber-bundles #group-cohomology #hopf-fibration #obstruction-theory

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