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Results tagged with at.algebraic-topology
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user 171227
Homotopy theory, homological algebra, algebraic treatments of manifolds.
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
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 …
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