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15
97
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trying to understand the connecting homomorphism between K theory groups

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#c-star-algebras #k-theory #topological-k-theory #algebraic-k-theory
392
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K-theory and usual (cohomoogical) Euler class

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#algebraic-topology #differential-topology #characteristic-classes #topological-k-theory
59
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Generators of $K_0(C(\mathbb{C}P^1))$

Published on
#c-star-algebras #k-theory #topological-k-theory
77
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$X/A\wedge Y/B= (X\times Y)/(X\times B\cup A\times Y)$

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#general-topology #algebraic-topology #homology-cohomology #vector-bundles #topological-k-theory
58
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unit element in cohomology and k-theory

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#differential-geometry #algebraic-topology #homology-cohomology #characteristic-classes #topological-k-theory
583
Views

Hatcher's, tensor product of vector bundles : topology explained

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#general-topology #algebraic-topology #vector-bundles #topological-k-theory
113
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Existence of an element in $K^0$ group, Koszul complexes

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#differential-geometry #algebraic-topology #vector-bundles #characteristic-classes #topological-k-theory
53
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the form of classes in $K(X)$ [Atiyah]

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#differential-geometry #algebraic-topology #homology-cohomology #vector-bundles #topological-k-theory
837
Views

Clutching function for $S^n$: why a vector bundle?

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#algebraic-topology #vector-bundles #topological-k-theory
264
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Operations on pullbacks of vector bundles.

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#general-topology #algebraic-topology #tensor-products #topological-k-theory
121
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Proving continuity of homotopy of clutching functions

Published on
#vector-bundles #topological-k-theory
91
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Explaining the $K$ functor isomorphism $K(X) \cong \tilde{K}(X) \oplus \Bbb Z$

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#algebraic-topology #direct-sum #topological-k-theory
105
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Short exact sequence of $K$ functor; applying Tietze extension

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#general-topology #analysis #vector-bundles #topological-k-theory
61
Views

two versions of the Euler class

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#homology-cohomology #vector-bundles #characteristic-classes #topological-k-theory
167
Views

Is $M \oplus e^1 = e^2$ , i.e. trivial?

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#algebraic-topology #vector-bundles #topological-k-theory

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