James numbers

Crabb, M. C.; Knapp, Karlheinz

doi:10.1007/bf01460042

Cited by 14 publications

(17 citation statements)

References 24 publications

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“…The numbers e(k, n) and e Sp (k, n) share many of the interesting properties of the slightly more basic numbers e U (k, n) studied in [13] and [11]. Computer algebra packages allow extensive computation of these numbers, uncovering patterns that cry out for generalization and proof.…”

Section: Applications To James Numbers and Exponentsmentioning

confidence: 99%

v₁-periodic homotopy groups ofSp(n)

Bendersky¹,

Davis²,

Mahowald³

1995

Pacific J. Math.

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Section: Applications To James Numbers and Exponentsmentioning

confidence: 99%

v₁-periodic homotopy groups ofSp(n)

Bendersky¹,

Davis²,

Mahowald³

1995

Pacific J. Math.

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“…The proof of part (1) of the following proposition can be found in Proposition (7.2) of [1], and Proposition (6.3) of [8]. Part (2) is an easy consequence of part (1), and can be found in Theorem (7.1) of [1], or with the use of K -theory in [4]. Proposition 4.1 Let the space A be a summand in the splitting of a suspended stunted complex projective space in Corollary 3.2.…”

Section: Exponentsmentioning

confidence: 99%

p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents

Beben

2010

Algebr. Geom. Topol.

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Let p be an odd prime, and fix integers m and n such that 0 < m < n Ä .p 1/.p 2/. We give a p -local homotopy decomposition for the loop space of the complex Stiefel manifold W n;m . Similar decompositions are given for the loop space of the real and symplectic Stiefel manifolds. As an application of these decompositions, we compute upper bounds for the p -exponent of W n;m . Upper bounds for p -exponents in the stable range 2m < n and 0 < m Ä .p

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“…One of the early references is [Lu,3.3]; in [CK1] and [CK2] much evidence is given to support the conjecture that if p is odd then DF;(n, k) = vp(Us(n+\,k+\)), and a modified version when p = 2. In [CK1,4.2], the equality of the RHS of our (3) for the multiplicative and canonical ^-typical FGL's is stated.…”

Section: Occurrences In Topologymentioning

confidence: 99%

“…In [CK1,4.2], the equality of the RHS of our (3) for the multiplicative and canonical ^-typical FGL's is stated. We thank Michael Crabb and Karlheinz Knapp for explaining several proofs of this fact, which were adapted to our proof.…”

Section: Occurrences In Topologymentioning

confidence: 99%