Resumen de Homotopy cardinality via extrapolation of Morava–Euler characteristics

Lior Yanovski

• 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 b-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.