Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On $ H\sb *(\Omega\sp {n+2}S\sp {n+1};{\bf F}\sb 2)$

Author: Thomas J. Hunter
Journal: Trans. Amer. Math. Soc. 314 (1989), 405-420
MSC: Primary 55P35; Secondary 55S12, 55T20
MathSciNet review: 946423
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Abstract: In this paper, we study $ {H_\ast}{\Omega ^{n + 2}}{S^{n + 1}}$ . Here $ \Omega X$ denotes the space of pointed maps $ {S^1} \to X$, and $ {H_\ast}$ represents homology modulo $ 2$. We show that the Eilenberg-Moore spectral sequence $ \operatorname{Tor}_{{H^\ast }\Omega _0^{n + 1}{S^{n + 1}}}^{\ast\ast}({F_{2,}}{F_2}) \Rightarrow {H^\ast }{\Omega ^{n + 2}}{S^{n + 1}}$ collapses, and we identify the kernel of the Whitehead product map $ {\Omega ^{n + 1}}{p_\ast}:{H_\ast}{\Omega ^{n + 3}}{S^{2n + 1}} \to {H_\ast}{\Omega ^{n + 1}}{S^n}$ . These observations yield two different descriptions of $ {H_\ast}{\Omega ^{n + 2}}{S^{n + 1}}$ up to extension.

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Article copyright: © Copyright 1989 American Mathematical Society