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Results tagged with at.algebraic-topology
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user 171227
Homotopy theory, homological algebra, algebraic treatments of manifolds.
5
votes
Injectivity of rationalization on spectrum morphisms
My comment, with more details: No, $E = H\mathbb{Q}$ and $F = \Sigma\mathbb{Z}$ gives a counterexample. $H_0(E) = \mathbb{Q}$ and $H_i(E) = 0$ for $i \neq 0$, so the universal coefficient theorem giv …
- 409
5
votes
Accepted
Multi-connected sum decomposition of $n$-manifolds
I don't have a reference, but I think it's not too hard to see that $M_1 \#_k M_2 \approx M_1 \# X_k \# M_2$, where $X_k = (S^1 \times S^{n-1})^{\# (k-1)}$. (Connected sum depends on choices of embed …
- 409
5
votes
Are finite $G$-spectra idempotent complete?
To complement Oscar's more systematic answer, let me expand my comment about the case $G = \mathbf{Z}/p\mathbf{Z}$ for a prime number $p$, where the answer is no when $\tilde{K}_0(\mathbf{Z}[G]) \neq …
11
votes
Accepted
Oriented cobordism classes represented by rational homology spheres
The necessary condition pointed out by Jens Reinhold is also sufficient: any torsion class $x = [M] \in \Omega^{SO}_d$ admits a representative where $M$ is a rational homology sphere.
EDIT: This is Th …
- 409