On J-orders of elements of KO(CPm)

Obiedat, Mohammad

doi:10.2969/jmsj/05340919

Cited by 2 publications

(4 citation statements)

References 7 publications

(13 reference statements)

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“…, 0)) for p = 2, 3 and then we obtain simple formulae for the 2 and 3 primary factors of the J-orders of the canonical generators of JO(CP m ). These simple formulae have been already conjectured in [9].…”

Section: Proof Since θOrmentioning

confidence: 53%

“…We will show how to use Formulae I and II of T O(X) (p) to find the J-orders of elements of KO(CP m ). As we have shown in [9], we only need to consider the case m is even, that is m = 2t for some t ∈ N. Let P m (y; m 1 , . .…”

Section: J-orders Of Elements Of Ko(cp M )mentioning

confidence: 99%

“…where j r = [ r−1 kp ] + 1. So, from (9), we need to find the smallest v which solves the following system of equations in Z (p) :…”

Section: Proof Since θOrmentioning

confidence: 99%

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A note on the localization of $J$-groups

Obiedat¹

1999

Hiroshima Math. J.

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Let JO(X) = KO(X)/T O(X) be the J-group of a connected finite CW complex X. Using Atiyah-Tall [5], we obtain two computable formulae of T O(X) (p) , the localization of T O(X) at a prime p. Then we show how to use those two formulae of T O(X) (p) to find the J-orders of elements of KO(X), at least the 2 and 3 primary factors of the canonical generators of JO(CP m ). Here CP m is the complex projective space. 1991 Mathematics Subject Classification: Primary 55Q50, 55R50.

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Section: Proof Since θOrmentioning

confidence: 53%

Section: J-orders Of Elements Of Ko(cp M )mentioning

confidence: 99%

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A note on the localization of $J$-groups

Obiedat¹

1999

Hiroshima Math. J.

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“…Because of [18], in this case (ℓ = 2, 3), we have KO(CP ℓ ) ≃ Z[y ℓ ]/ y 2 ℓ , where y ℓ = r(γ)−2 for the canonical line bundle γ and the realification map r : K(CP ℓ ) → KO(CP ℓ ). Moreover, we have r(γ ⊗n ) = n 2 y ℓ + 2 by [18]. Hence, for i = 1, 2, we have that…”

Section: Casementioning

confidence: 99%

Topological classification of torus manifolds which have codimension one extended actions

Choi

Kuroki

2011

Algebr. Geom. Topol.

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A toric manifold is a compact non-singular toric variety equipped with a natural half-dimensional compact torus action. A torus manifold is an oriented, closed, smooth manifold of dimension 2n with an effective action of a compact torus T n having a non-empty fixed point set. Hence, a torus manifold can be thought of as a generalization of a toric manifold. In the present paper, we focus on a certain class M in the family of torus manifolds with codimension one extended actions, and we give a topological classification of M. As a result, their topological types are completely determined by their cohomology rings and real characteristic classes.The problem whether the cohomology ring determines the topological type of a toric manifold or not is one of the most interesting open problems in toric topology. One can also ask this problem for the class of torus manifolds even if its orbit spaces are highly structured. Our results provide a negative answer to this problem for torus manifolds. However, we find a sub-class of torus manifolds with codimension one extended actions which is not in the class of toric manifolds but which is classified by their cohomology rings.

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On J-orders of elements of KO(CPm)

Cited by 2 publications

References 7 publications

A note on the localization of $J$-groups

A note on the localization of $J$-groups

Topological classification of torus manifolds which have codimension one extended actions

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