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Results tagged with kt.k-theory-and-homology
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user 9684
Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
7
votes
The complex $K$-theory of the Thom spectrum $MU$
You can learn about this, and more, in Part II of Adams' "Stable Homotopy and Generalised Homology" (1974), especially section 4, in the special case $E = KU$.
- 9,263
4
votes
Injectivity of assembly in A-theory for $BC_2 = \mathbb R P^\infty$ in degree $4$
Not an answer, but a possible approach: Using Dundas' cartesian square with corners $A(*)$, $K(Z)$, $TC(*)$ and $TC(Z)$ you can see that $Wh^{Diff}_3(*) = Z/2$ comes from $TC_4(Z) = Z/8$ (plus odd tor …
- 9,263
8
votes
Good reference for topological Hochschild homology
Ib Madsen's survey
MR1474979 (98g:19004) Madsen, Ib Algebraic K-theory and traces.
Current developments in mathematics, 1995 (Cambridge, MA), 191–321,
Int. Press, Cambridge, MA, 1994.
was written to …
- 9,263
5
votes
Accepted
Torsion In $K$ theory on simply connected manifolds
Let $X$ be a $2$-connected closed $7$-manifold with $H_3(X) = H^4(X) = \mathbb{Z}/2$. Then $\tilde K(X) = \widetilde{KU}^0(X)$ equals $\mathbb{Z}/2$. This follows from the Atiyah--Hirzebruch spectra …
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28
votes
Does Milnor K-Theory arise from Waldhausen K-Theory
Bob Thomason proved that there is no Milnor K-theory functor for schemes,
with a reasonable map to Quillen K-theory, in:
Le principe de scindage et
l'inexistence d'une $K$-theorie de
Milnor gl …
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13
votes
Morava on Shafarevich conjecture
(3) The statement is that the map of ring spectra $S \to HZ$ induces a rational equivalence $K(S) \to K(Z)$. A reference is Proposition 2.2 in:
Waldhausen, Friedhelm: Algebraic
$K$-theory of to …
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16
votes
Is there a simple relationship between K-theory and Galois theory?
A simpler statement may be that if $F \to E$ is a $G$-Galois extension, then
there is a map $K(F) \to K(E)^{hG}$ from the algebraic $K$-theory space of $F$
to the $G$-homotopy fixed points of the alge …
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