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K-theory functoriality understanding

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#category-theory #abelian-groups #functors #k-theory #topological-k-theory
141
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Compute the $K$-theories of crossed products $K_0(C_0(\mathbb N\times G)\rtimes_r G)$ and $K_0(\ell^\infty(\mathbb N,C_0(G))\rtimes_r G)$

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#operator-algebras #c-star-algebras #direct-sum #k-theory
77
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Let $h,h'$ be hermitian metric over vector space $V$, then grassmanian $G_n(V_h)\to G_n(V_{h'})$ is always continuous?

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#differential-geometry #algebraic-topology #k-theory #grassmannian #topological-k-theory
50
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$C^m\to C^{m-1}$ projection map projecting out last factor inducing $G_n(C^{m-1})\to G_n(C^m)$?

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#algebraic-topology #k-theory #grassmannian #topological-k-theory
204
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Complex line bundles with connection can be parametrized by unitary character of fundamental group

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#mathematical-physics #complex-geometry #symplectic-geometry #k-theory #topological-k-theory
45
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the semigroup $D(\Bbb C)$

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#operator-algebras #c-star-algebras #k-theory #algebraic-k-theory
103
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a unitary does not in general lift to a unitary

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#c-star-algebras #k-theory #topological-k-theory #algebraic-k-theory
121
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Equivalence of categories of coherent sheaves

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#algebraic-geometry #k-theory #algebraic-k-theory
32
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the isomorphism of $D(B(H))$,where ,$H$ is an infinite dimensional inseparable Hilbert space.

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#c-star-algebras #k-theory #topological-k-theory #algebraic-k-theory
51
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a surjective group homomorphism between $K_0$ group to an abelian group

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#operator-theory #operator-algebras #c-star-algebras #k-theory
183
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cone of a $C^*$-algebra

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#operator-theory #operator-algebras #c-star-algebras #k-theory
102
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Functoriality of twisted K-theory

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#homology-cohomology #k-theory #topological-k-theory #stable-homotopy-theory #spectra
215
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the $K_0$ group of von Neumann algebra factor of type $II_{\infty}$ and type $III$

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#operator-algebras #c-star-algebras #von-neumann-algebras #k-theory
85
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Relation between $G$ bundle over free $G$ space $X$ and vector bundles over $X/G$ (Atiyah)

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#differential-geometry #vector-bundles #k-theory
243
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Notation in Serge Lang - Algebra

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#abstract-algebra #algebraic-topology #homological-algebra #homotopy-theory #k-theory

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