 Mapping-telescope realization of the rational group with square-free denominators

ID: mapping-telescope-realization-of-the-rational-group-with-square-free-denominators

List the primes as

p_{0}, p_{1}, \dots

and form the mapping telescope of degree-

p_{i}

S^{n} \to S^{n}

. Its reduced homology vanishes outside degree

n

, while

H_{n} (T; Z) ≅ lim (Z p_{0} Z p_{1} \dots) ≅ Q_{sq} .

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