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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
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.
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Yves
Félix and Stephen
Halperin, Rational LS category and its
applications, Trans. Amer. Math. Soc.
273 (1982), no. 1,
1–38. MR
664027 (84h:55011), http://dx.doi.org/10.1090/S0002-9947-1982-0664027-0
- [FHLT]
Yves
Félix, Stephen
Halperin, Jean-Michel
Lemaire, and Jean-Claude
Thomas, Mod 𝑝 loop space homology, Invent. Math.
95 (1989), no. 2, 247–262. MR 974903
(89k:55010), http://dx.doi.org/10.1007/BF01393897
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T.
Ganea, Lusternik-Schnirelmann category and strong category,
Illinois J. Math. 11 (1967), 417–427. MR 0229240
(37 #4814)
- [Gi]
Michael
Ginsburg, On the Lusternik-Schnirelmann category, Ann. of
Math. (2) 77 (1963), 538–551. MR 0149489
(26 #6976)
- [He]
Kathryn
P. Hess, A proof of Ganea’s conjecture for rational
spaces, Topology 30 (1991), no. 2,
205–214. MR 1098914
(92d:55012), http://dx.doi.org/10.1016/0040-9383(91)90006-P
- [HL]
S.
Halperin and J.-M.
Lemaire, Notions of category in differential algebra,
Algebraic topology—rational homotopy (Louvain-la-Neuve, 1986)
Lecture Notes in Math., vol. 1318, Springer, Berlin, 1988,
pp. 138–154. MR 952577
(89h:55023), http://dx.doi.org/10.1007/BFb0077800
- [S]
Paul
A. Schweitzer, Secondary cohomology operations induced by the
diagonal mapping, Topology 3 (1965), 337–355.
MR
0182969 (32 #451)
- [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)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1992-1093598-X
PII:
S 0002-9939(1992)1093598-X
Keywords:
Milnor Moore spectral sequence,
Lusternik-Schnirelmann category,
free tensor model
Article copyright:
© Copyright 1992 American Mathematical Society
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