Timeline for Convergence of a sum with the ranks of homotopy groups
Current License: CC BY-SA 3.0
3 events
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| May 25, 2015 at 19:25 | comment | added | David C | You are right this paper considers sums of the form $$\sum_{q=k+2}^{k+n} Rank(\pi_q(X)).$$ This is related to the elliptic/hyperbolic dichotomy in homotopy theory. Your sum is convergent in the elliptic case. | |
| May 25, 2015 at 19:18 | comment | added | user62675 | David, correct me if I'm mistaken, but this paper considers the sum of the ranks, i.e., $\sum\mathrm{Rank}(\pi_q(F))$, not $\sum\frac{\mathrm{Rank}(\pi_q(F))}{q}$. (The denominator in the expression is like a "normalization".) | |
| May 25, 2015 at 19:10 | history | answered | David C | CC BY-SA 3.0 |