TY - JOUR
T1 - Homotopy cardinality via extrapolation of Morava–Euler characteristics
AU - Yanovski, Lior
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2023/11
Y1 - 2023/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85175076554&partnerID=8YFLogxK
U2 - 10.1007/s00029-023-00886-3
DO - 10.1007/s00029-023-00886-3
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AN - SCOPUS:85175076554
SN - 1022-1824
VL - 29
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 5
M1 - 81
ER -