On the groups J(X). IV

Adams, J. F.; Shepherd, G. C.

doi:10.1017/cbo9780511662584.023

Cited by 77 publications

(259 citation statements)

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“…Our notion of spectra is very naive, and we refer the reader to [3,4] for an introduction to CW spectra. The only difference between these and the spectra we use is that each level of our spectra is in fact a compact Hausdorff space and the structure maps are only assumed to be continuous.…”

Section: Construction Of the Floer Homotopy Typementioning

confidence: 99%

On the immersion classes of nearby Lagrangians: Table 1.

Abouzaid

Kragh²

2015

J Topology

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Abstract. We show that the transfer map on Floer homotopy types associated to an exact Lagrangian embedding is an equivalence. This provides an obstruction to representing isotopy classes of Lagrangian immersions by Lagrangian embeddings, which, unlike previous obstructions, is sensitive to information that cannot be detected by Floer cochains. We show this by providing a concrete computation in the case of spheres.

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Section: Construction Of the Floer Homotopy Typementioning

confidence: 99%

On the immersion classes of nearby Lagrangians: Table 1.

Abouzaid

Kragh²

2015

J Topology

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“…In other words, the ψ 3 e-invariant (see [1]) of C(Θ 2j ) is half that of RP 2j+1 in Example 3.2, which is the mapping cone of θ in the canonical cofibre sequence…”

Section: Proofmentioning

confidence: 99%

Upper Triangular Technology and the Arf-Kervaire Invariant

Snaith¹

2009

Stable Homotopy Around the Arf-Kervaire Invariant

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Abstract. This paper introduces the upper triangular technology (UTT) into classical homotopy theory. This is a new and easy to use method to calculate the effect of the left unit map in 2-adic connective K-theory; the map which is the basis for operations in bu-theory. By way of application, UTT is used to give a new, very simple proof of a conjecture of BarrattJones-Mahowald, which rephrases K-theoretically the existence of framed manifolds of Arf-Kervaire invariant one.

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“…Let M p -S° U p e 1 be the mod-p Moore spectrum, A: 1 q M P^> M P an Adams periodicity map (see 1991 Mathematics Subject Classification: 55N15, 55N20, 55P42, 55S25. [2] or [7]), and V(l) the cofibre of A. Then Z(n) is a wedge of suspensions of K(l).…”

Section: Introductionmentioning

confidence: 99%