New estimates for the collapse of the Milnor-Moore spectral sequence over a field

Jessup, Barry

doi:10.1090/S0002-9939-1992-1093598-X

New estimates for the collapse of the Milnor-Moore spectral sequence over a field

Author: Barry Jessup
Journal: Proc. Amer. Math. Soc. 114 (1992), 1115-1117
MSC: Primary 55M30; Secondary 55P50, 55P60, 55P62
DOI: https://doi.org/10.1090/S0002-9939-1992-1093598-X
MathSciNet review: 1093598
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Abstract: We use the free tensor models of Halperin and Lemaire to give a new and transparent proof of a theorem of Ginsburg's on the collapse of the Milnor-Moore spectral under the assumption of finite L.-S. category. The method, valid over any field, provides better bounds for the collapse and these bounds are effectively computable L.-S. type invariants.

[FH] Y. Felix and S. Halperin, Rational L.-S. category and its applications, Trans. Amer. Math. Soc. 273 (1982), 1-37. MR 664027 (84h:55011)
[FHLT] Y. Felix, S. Halperin, J. M. Lemaire, and J. C. Thomas, loop space homology, Inventiones Math. 95 (1989), 247-262. MR 974903 (89k:55010)
[G] T. Ganea, Lusternik-Schnirelmann category and strong category, Illinois J. Math 11 (1967), 417-427. MR 0229240 (37:4814)
[Gi] M. Ginsburg, On the L.S. category, Ann. of Math. 77 (1963), 538-551. MR 0149489 (26:6976)
[He] K. Hess, A proof of Ganea's conjecture for rational spaces, Topology Vol. 30, No. 2, pp. 205-214, 1991. MR 1098914 (92d:55012)
[HL] S. Halperin and J.-M. Lemaire, Notions of category in differential algebra, Lecture Notes in Math., vol. 1318, Springer-Verlag, Berlin, 1988, pp. 138-154. MR 952577 (89h:55023)
[S] P. A. Schweitzer, Secondary cohomology operations induced by the diagonal mapping, Topology 3 (1965), 337-355. MR 0182969 (32:451)