Homotopy cardinality via extrapolation of Morava–Euler characteristics

Lior Yanovski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We answer a question of John Baez, on the relationship between the classical Euler characteristic and the Baez–Dolan homotopy cardinality, by constructing a unique additive common generalization after restriction to an odd prime p. This is achieved by ℓ -adically extrapolating to height n= - 1 the sequence of Euler characteristics associated with the Morava K(n) cohomology theories for (any) ℓ∣ p- 1 . We compute this sequence explicitly in several cases and incorporate in the theory some folklore heuristic comparisons between the Euler characteristic and the homotopy cardinality involving summation of divergent series.

Original languageAmerican English
Article number81
JournalSelecta Mathematica, New Series
Issue number5
StatePublished - Nov 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.


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