H-Spaces With Noetherian Mod Two Cohomology Algebra

Broto, Carles; Crespo, Juan A.

doi:10.1016/s0040-9383(98)00017-2

Cited by 12 publications

(38 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First we determine the homotopy type of a simply connected homotopy associative and homotopy commutative mod 3 finite H-space (see Proposition 3.1). By using Proposition 3.1, Proposition 2.3 and results of Broto and Crespo [5], [8], we can prove Theorem A. Next we complete the proof of Corollary 1.2 by using a spectral sequence argument.…”

Section: Proof Of Theorem Amentioning

confidence: 69%

“…In §3 we prove Theorem A and Corollary 1.2. By combining Proposition 2.3 with results of Broto and Crespo [5], [8], we can reduce Theorem A to the case of mod 3 finite H-spaces. From a result of Lin [17], we can determine the homotopy type of a homotopy associative and homotopy commutative mod 3 finite H-space (see Proposition 3.1).…”

Section: ]) If Sp(2) 3;mentioning

confidence: 86%

“…By using Proposition 2.3, Proposition 3.1 and results of Broto and Crespo [5], [8], we can prove Theorem A as follows:…”

Section: Proof Of Proposition 31 By Lemma 32 There Exist Maps Fmentioning

confidence: 92%

“…[5], [8], [13], [14], [16], [22], [23]). Recently, Broto and Crespo [5], [8] gave an important result for H-spaces with finitely generated cohomology. They have shown that such an H-space is the total space of an H-fibration over a finite Hspace.…”

Section: Introductionmentioning

confidence: 99%

“…Broto-Crespo [5] reproved the above theorem by using another method. At odd primes, it is known that any connected mod p H-space admits an H-structure which is homotopy commutative by a result of Iriye-Kono [10].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Homotopy commutativity of $H$-spaces with finitely generated cohomology

Kawamoto

Lin

2001

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. We show that a simply connected homotopy associative and homotopy commutative mod 3 H-space with finitely generated mod 3 cohomology is homotopy equivalent to a finite product of K(Z, 2), Sp(2), the threeconnected cover Sp(2) 3 and the homotopy fiber Sp(2) 3; 3 i of the map [3 i ] : Sp(2) → K(Z, 3) for i ≥ 1. Our result also shows that a connected Cp-space in the sense of Sugawara with finitely generated mod p cohomology has the homotopy type of a finite product of K(Z, 1), K(Z, 2) and K(Z/p i , 1) for i ≥ 1.

show abstract

Section: Proof Of Theorem Amentioning

confidence: 69%

Section: ]) If Sp(2) 3;mentioning

confidence: 86%

“…By using Proposition 2.3, Proposition 3.1 and results of Broto and Crespo [5], [8], we can prove Theorem A as follows:…”

Section: Proof Of Proposition 31 By Lemma 32 There Exist Maps Fmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Homotopy commutativity of $H$-spaces with finitely generated cohomology

Kawamoto

Lin

2001

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

Structure of mod p H-spaces with finiteness conditions

Crespo

2001

Cohomological Methods in Homotopy Theory

View full text Add to dashboard Cite

The topological nilpotence degree of a Noetherian unstable algebra

Heard

2021

Sel. Math. New Ser.

View full text Add to dashboard Cite

We investigate the topological nilpotence degree, in the sense of Henn–Lannes–Schwartz, of a connected Noetherian unstable algebra R. When R is the mod p cohomology ring of a compact Lie group, Kuhn showed how this invariant is controlled by centralizers of elementary abelian p-subgroups. By replacing centralizers of elementary abelian p-subgroups with components of Lannes’ T-functor, and utilizing the techniques of unstable algebras over the Steenrod algebra, we are able to generalize Kuhn’s result to a large class of connected Noetherian unstable algebras. We show how this generalizes Kuhn’s result to more general classes of groups, such as groups of finite virtual cohomological dimension, profinite groups, and Kac–Moody groups. In fact, our results apply much more generally, for example, we establish results for p-local compact groups in the sense of Broto–Levi–Oliver, for connected H-spaces with Noetherian mod p cohomology, and for the Borel equivariant cohomology of a compact Lie group acting on a manifold. Along the way we establish several results of independent interest. For example, we formulate and prove a version of Carlson’s depth conjecture in the case of a Noetherian unstable algebra of minimal depth.

show abstract

H-Spaces With Noetherian Mod Two Cohomology Algebra

Cited by 12 publications

References 18 publications

Homotopy commutativity of $H$-spaces with finitely generated cohomology

Homotopy commutativity of $H$-spaces with finitely generated cohomology

Structure of mod p H-spaces with finiteness conditions

The topological nilpotence degree of a Noetherian unstable algebra

Contact Info

Product

Resources

About