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arXiv · 2303.10258

Kunneth formulas for Cotor

A. Salch
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Abstract

We investigate the question of how to compute the cotensor product, and more generally the derived cotensor (i.e., Cotor) groups, of a tensor product of comodules. In particular, we determine the conditions under which there is a K\"{u}nneth formula for Cotor. We show that there is a simple K\"{u}nneth theorem for Cotor groups if and only if an appropriate coefficient comodule has trivial coaction. This result is an application of a spectral sequence we construct for computing Cotor of a tensor product of comodules. Finally, for certain families of nontrivial comodules which are especially topologically natural, we work out necessary and sufficient conditions for the existence of a K\"{u}nneth formula for the $0$th Cotor group, i.e., the cotensor product. We give topological applications in the form of consequences for the $E_2$-term of the Adams spectral sequence of a smash product of spectra, and the Hurewicz image of a smash product of spectra.

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A. Salch. 2023-03-17. Kunneth formulas for Cotor. https://arxiv.org/abs/2303.10258

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