Algebraic structure in the loop space homology Bockstein spectral sequence

Author:
Jonathan A. Scott

Journal:
Trans. Amer. Math. Soc. **354** (2002), 3075-3084

MSC (2000):
Primary 55P35; Secondary 16S30

DOI:
https://doi.org/10.1090/S0002-9947-02-02971-9

Published electronically:
April 1, 2002

MathSciNet review:
1897391

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite, -dimensional, -connected CW complex. We prove the following theorem:

If is an odd prime, then the loop space homology Bockstein spectral sequence modulo is a spectral sequence of universal enveloping algebras over differential graded Lie algebras.

**1.**M. André,*Hopf algebras with divided powers*, J. Algebra**18**(1971), 19-50. MR**43:3323****2.**David J. Anick,*Hopf algebras up to homotopy*, J. Amer. Math. Soc.**2**(1989), no. 3, 417-453. MR**90c:16007****3.**William Browder,*Torsion in -spaces*, Ann. of Math. (2)**74**(1961), 24-51. MR**23:A2201****4.**Y. Félix, S. Halperin, and J.-C. Thomas,*Differential graded algebras in topology*, Handbook of Algebraic Topology, North-Holland, Amsterdam, 1995, pp. 829-865. MR**96j:57052****5.**Stephen Halperin,*Universal enveloping algebras and loop space homology*, J. Pure Appl. Alg.**83**(1992), 237-282. MR**93k:55014****6.**John W. Milnor and John C. Moore,*On the structure of Hopf algebras*, Ann. of Math. (2)**81**(1965), 211-264. MR**30:4259****7.**Gunnar Sjödin,*Hopf algebras and derivations*, J. Algebra**64**(1980), 218-229. MR**84a:16016**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (2000):
55P35,
16S30

Retrieve articles in all journals with MSC (2000): 55P35, 16S30

Additional Information

**Jonathan A. Scott**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3, Canada

Address at time of publication:
Aberdeen Topology Centre, Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

Email:
j.scott@maths.abdn.ac.uk

DOI:
https://doi.org/10.1090/S0002-9947-02-02971-9

Keywords:
Loop space homology,
Bockstein spectral sequence,
universal enveloping algebra

Received by editor(s):
November 1, 2001

Published electronically:
April 1, 2002

Article copyright:
© Copyright 2002
American Mathematical Society