On the size of the third homotopy group of the suspension of an Eilenberg--MacLane space

Niroomand, Peyman; Russo, Francesco G.

doi:10.3906/mat-1302-50

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…Many authors have studied bounds on the order of π 3 (SK (G, 1)) (cf. [1,6,7,17]). We deduce a finiteness criterion for π 3 (S X) in terms of π 2 (X ) and the number of tensors T ⊗ (G), where π 1 (X ) ∼ = G and S X is the suspension of the space X (see Remark 2.4).…”

Section: Theorem a Let X Be A Union Of Open Subspaces A B Such That mentioning

confidence: 99%

Finiteness of homotopy groups related to the non-abelian tensor product

Bastos

Rocco

Vieira

2019

Annali di Matematica

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Using finiteness-related results for non-abelian tensor products, we prove finiteness conditions for the homotopy groups π n (X) in terms of the number of tensors. In particular, we establish a quantitative version of the classical Blakers-Massey triad connectivity theorem. Moreover, we study other finiteness conditions and equivalence properties that arise from the non-abelian tensor square. Finally, we give applications to homotopy pushouts, especially in the case of Eilenberg-MacLane spaces.

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Section: Theorem a Let X Be A Union Of Open Subspaces A B Such That mentioning

confidence: 99%

Finiteness of homotopy groups related to the non-abelian tensor product

Bastos

Rocco

Vieira

2019

Annali di Matematica

View full text Add to dashboard Cite

show abstract

“…Many authors had studied bounds to the order of π 3 (SK(G, 1)) (cf. [1,6,7,17]). Now, we can deduce a finiteness criterion for π 3 (SX) in terms of π 2 (X) and the number of tensors T ⊗ (G), where π 1 (X) ∼ = G and SX is the suspension of a space X (see Remark 2.4, below).…”

Section: An Application Of Theoremmentioning

confidence: 99%

Finiteness of homotopy groups related to the non-abelian tensor product

Bastos,

Rocco,

Vieira

2018

Preprint

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By using finiteness related result of non-abelian tensor product we prove finiteness conditions for the homotopy groups π n (X) in terms of the number of tensors. In particular, we establish a quantitative version of the classical Blakers-Massey triad connectivity theorem. Moreover, we study others finiteness conditions and equivalence properties that arise from the non-abelian tensor square. In the end, we give applications to homotopy pushout, especially in the case of Eilenberg-MacLane spaces.

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Decomposition of the Nonabelian Tensor Product of Lie Algebras via the Diagonal Ideal

Niroomand

Johari

Parvizi

et al. 2017

Bull. Malays. Math. Sci. Soc.

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Abstract. We prove a theorem of splitting for the nonabelian tensor product L ⊗ N of a pair (L, N ) of Lie algebras L and N in terms of its diagonal ideal L N and of the nonabelian exterior product L ∧ N . A similar circumstance was described two years ago by the second author in the special case N = L. The interest is due to the fact that the size of L N influences strongly the structure of L ⊗ N . Another question, often related to the structure of L ⊗ N , deals with the behaviour of the operator with respect to the formation of free products. We answer with another theorem of splitting even in this case, noting some connections with the homotopy theory.

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On the size of the third homotopy group of the suspension of an Eilenberg--MacLane space

Cited by 6 publications

References 13 publications

Finiteness of homotopy groups related to the non-abelian tensor product

Finiteness of homotopy groups related to the non-abelian tensor product

Finiteness of homotopy groups related to the non-abelian tensor product

Decomposition of the Nonabelian Tensor Product of Lie Algebras via the Diagonal Ideal

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