2017
DOI: 10.1016/j.topol.2017.08.010
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Characteristic rank of canonical vector bundles over oriented Grassmann manifolds G˜3,n

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Cited by 5 publications
(8 citation statements)
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“…We note that Theorem A (cf. Theorem 3.4 in this article) gives a different proof of Theorem 1.1 of [11].…”
Section: Theorem a (A)mentioning
confidence: 85%
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“…We note that Theorem A (cf. Theorem 3.4 in this article) gives a different proof of Theorem 1.1 of [11].…”
Section: Theorem a (A)mentioning
confidence: 85%
“…Due to [4] and [11], we know the degree of the first indecomposable element of H * ( G n,3 ; Z 2 ) after degree 3. In this article we determine the complete set of degrees of indecomposables in H * ( G n,3 ; Z 2 ) (cf.…”
Section: Introductionmentioning
confidence: 99%
“…Although the characteristic rank of γ n,3 is already known [10], together with the corresponding result on cup-length, we will explicitly derive the values implied by Theorem 4.1 in this case. The intent is to allow us to discuss certain aspects of the proof, which generalize to the case of arbitrary k. Proof.…”
Section: The Resultsmentioning
confidence: 99%
“…In particular, the paper by Fukaya [2] (where a slightly different notation for Grassmann manifolds is used; G n,3 corresponds to G n+3,3 in this paper) contains the proof, that cup( G 2 t −1,3 ) = 2 t − 3 for t ≥ 3, and the following interesting conjecture [ The value cup( G 2 t −1,3 ) = 2 t − 3 has been obtained independently by Korbaš [4] employing an approach using the notion of characteristic rank. Making use of refined version of this idea, some other parts of the conjecture have been proved in papers [10], [11]. Namely, the cases corresponding to n in the interval 2 t −1 ≤ n < 2 t −1+ 2 t 3 for t ≥ 3 and n = 2 t + 2 t−1 + a for a = 1, 2 and t ≥ 3.…”
Section: Introductionmentioning
confidence: 99%
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