The homotopy groups of a homotopy group completion
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DOI: 10.1007/s11856-019-1914-2
Abstract: Let $M$ be a topological monoid with homotopy group completion $\Omega BM$. Under a strong homotopy commutativity hypothesis on $M$, we show that $\pi_k (\Omega BM)$ is the quotient of the monoid of free homotopy… read more here.
Keywords: homotopy groups; group completion; homotopy; homotopy group ... See more keywords
A Whitehead theorem for periodic homotopy groups
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DOI: 10.1007/s11856-021-2086-4
Abstract: We show that v n -periodic homotopy groups detect homotopy equivalences between simply-connected finite CW-complexes. read more here.
Keywords: whitehead theorem; periodic homotopy; theorem periodic; homotopy groups ... See more keywords
A theorem on multiplicative cell attachments with an application to Ravenel’s X(n) spectra
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DOI: 10.1007/s40062-018-0222-6
Abstract: We show that the homotopy groups of a connective $$\mathbb {E}_k$$Ek-ring spectrum with an $$\mathbb {E}_k$$Ek-cell attached along a class $$\alpha $$α in degree n are isomorphic to the homotopy groups of the cofiber of… read more here.
Keywords: theorem multiplicative; homotopy groups; ravenel spectra; mathbb ... See more keywords
Bounding size of homotopy groups of Spheres
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DOI: 10.1017/s001309152000036x
Abstract: Abstract Let p be prime. We prove that, for n odd, the p-torsion part of πq(Sn) has cardinality at most $p^{2^{{1}/({p-1})(q-n+3-2p)}}$ and hence has rank at most 21/(p−1)(q−n+3−2p). for p = 2, these results also… read more here.
Keywords: homotopy; bounding size; homotopy groups; size homotopy ... See more keywords