Homotopy cardinality via extrapolation of Morava–Euler characteristics

• Lior Yanovski ^[1]
  1. [1] Hebrew University of Jerusalem

     Hebrew University of Jerusalem

     Israel

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 5, 2023
• Idioma: inglés
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• Resumen

  • 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.