Continuous homology of topological periodic homology of complex cobordism

Sverre Lunøe-Nielsen; John Rognes

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arXiv · 2606.30240

Continuous homology of topological periodic homology of complex cobordism

Sverre Lunøe-Nielsen·John Rognes

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Abstract

We determine the continuous mod $p$ homology of the topological periodic homology $TP(MU)$ of the complex cobordism spectrum, as a graded algebra with Steenrod operations. The answer is given in terms of an explicit and purely algebraic construction $C_+$, analogous to Singer's construction $R_+$. Its $Ext$-algebra provides the $E_2$-term for a multiplicative Adams-type spectral sequence converging strongly to the homotopy of $p$-completed $TP(MU)$.

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BibTeX RIS

Sverre Lunøe-Nielsen, John Rognes. 2026-06-29. Continuous homology of topological periodic homology of complex cobordism. https://arxiv.org/abs/2606.30240

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