On rationalized H- and co-H-spaces with an appendix on decomposable H- and co-H-spaces

Scheerer, Hans

doi:10.1007/bf01168347

Cited by 37 publications

(22 citation statements)

References 17 publications

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“…Moreover, by Example 7.6, the complete Lie algebra E * (Y ){2k + 1} satisfies condition (44). Likewise, we know from (33) that…”

Section: Groups Of Homotopy Groupsmentioning

confidence: 89%

“…Obviously, the mlie L * (X) also satisfies (44). From the Lazard formula (46), we infer that the grlie's gr *…”

Section: Groups Of Homotopy Groupsmentioning

confidence: 94%

“…From Proposition 6.10 and Theorem 6.2, we know that the group Hom coalg (H * (ΩS 2 , Q), H * (ΩY, Q)), endowed with the Cohen-Gitler filtration (11) is isomorphic to exp(E * (Y ){2} ), where E * (Y ){2} is filtered as in (36). By Example 7.6, this filtration satisfies condition (44).…”

Section: The Loop Space Of S 2 Againmentioning

confidence: 99%

“…Thus, we may use Proposition 1 in Scheerer [44] to conclude that the Hurewicz map h Q is a group isomorphism.…”

Section: Proof Of Theorem Dmentioning

confidence: 99%

“…(When Y is a Q-local space, this group is in fact isomorphic to [K, ΩY ]; see [44].) There is a natural filtration on the group (10), with r-th term equal to…”

Section: Lcs Formula For Higher Homotopy Groupsmentioning

confidence: 99%

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Homotopy Lie algebras, lower central series and the Koszul property

Papadima

Suciu

2004

Geom. Topol.

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Let X and Y be finite-type CW-complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k -rescaling of the rational cohomology ring of X . Assume H * (X, Q) is a Koszul algebra. Then, the homotopy Lie algebra π * (ΩY ) ⊗ Q equals, up to k -rescaling, the graded rational Lie algebra associated to the lower central series of π 1 (X). If Y is a formal space, this equality is actually equivalent to the Koszulness of H * (X, Q). If X is formal (and only then), the equality lifts to a filtered isomorphism between the Malcev completion of π 1 (X) and the completion of [ΩS 2k+1 , ΩY ]. Among spaces that admit naturally defined homological rescalings are complements of complex hyperplane arrangements, and complements of classical links. The Rescaling Formula holds for supersolvable arrangements, as well as for links with connected linking graph. AMS Classification numbers Primary: 16S37, 20F14, 55Q15Secondary: 20F40, 52C35, 55P62, 57M25, 57Q45

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“…Moreover, by Example 7.6, the complete Lie algebra E * (Y ){2k + 1} satisfies condition (44). Likewise, we know from (33) that…”

Section: Groups Of Homotopy Groupsmentioning

confidence: 89%

“…Obviously, the mlie L * (X) also satisfies (44). From the Lazard formula (46), we infer that the grlie's gr *…”

Section: Groups Of Homotopy Groupsmentioning

confidence: 94%

Section: The Loop Space Of S 2 Againmentioning

confidence: 99%

“…Thus, we may use Proposition 1 in Scheerer [44] to conclude that the Hurewicz map h Q is a group isomorphism.…”

Section: Proof Of Theorem Dmentioning

confidence: 99%

“…(When Y is a Q-local space, this group is in fact isomorphic to [K, ΩY ]; see [44].) There is a natural filtration on the group (10), with r-th term equal to…”

Section: Lcs Formula For Higher Homotopy Groupsmentioning

confidence: 99%

See 3 more Smart Citations