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Torsion exponents in stable homotopy and the Hurewicz homomorphism | | Akhil Mathew
; | | Date: |
29 Jan 2015 | | Abstract: | We give estimates for the torsion in the Postnikov sections $ au_{[1, n]}
S^0$ of the sphere spectrum, and show that the $p$-localization is annihilated
by $p^{n/(2p-2) + O(1)}$. This leads to explicit bounds on the exponents of the
kernel and cokernel of the Hurewicz map $pi_*(X) o H_*(X; mathbb{Z})$ for a
connective spectrum $X$. Such bounds were first considered by Arlettaz,
although our estimates are tighter and we prove that they are the best possible
up to a constant factor. As applications, we sharpen existing bounds on the
orders of $k$-invariants in a connective spectrum, sharpen bounds on the
unstable Hurewicz of an infinite loop space, and prove an exponent theorem for
the equivariant stable stems. | | Source: | arXiv, 1501.7561 | | Services: | Forum | Review | PDF | Favorites | |
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