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anomaly
anomaly
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If $M$ is torsion-free (as a $\mathbb{Z}-$module), then the Kunneth formula still holds. If $M$ is the$M = \mathbb{Z}$ with trivial $\mathbb{Z}$-modulegroup action, then it holds by the corresponding result for the CW-complex category and abstract nonsense; more generally, it holds for chain complexes under some fairly mild restrictions (including having finite homology in each dimension, but that's clear here.)

If $M$ is torsion-free (as a $\mathbb{Z}-$module), then the Kunneth formula still holds. If $M$ is the trivial $\mathbb{Z}$-module, then it holds by the corresponding result for the CW-complex category and abstract nonsense; more generally, it holds for chain complexes under some fairly mild restrictions (including having finite homology in each dimension, but that's clear here.)

If $M$ is torsion-free (as a $\mathbb{Z}-$module), then the Kunneth formula still holds. If $M = \mathbb{Z}$ with trivial group action, then it holds by the corresponding result for the CW-complex category and abstract nonsense; more generally, it holds for chain complexes under some fairly mild restrictions (including having finite homology in each dimension, but that's clear here.)

Source Link
anomaly
anomaly
  • 432
  • 6
  • 17

If $M$ is torsion-free (as a $\mathbb{Z}-$module), then the Kunneth formula still holds. If $M$ is the trivial $\mathbb{Z}$-module, then it holds by the corresponding result for the CW-complex category and abstract nonsense; more generally, it holds for chain complexes under some fairly mild restrictions (including having finite homology in each dimension, but that's clear here.)