|
Emergence of the Witt group in the cellular lattice of rational spaces
Author(s):
Kathryn
Hess;
Paul-Eugène
Parent
Journal:
Trans. Amer. Math. Soc.
354
(2002),
4571-4583.
MSC (2000):
Primary 11E04, 55P60, 55P62
Posted:
July 2, 2002
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give an embedding of a quotient of the Witt semigroup into the lattice of rational cellular classes represented by formal  -cones between  and the two-cell complex ![$X_n=S^{2n}\cup_{[\iota,\iota]}e^{4n}$](/tran/2002-354-11/S0002-9947-02-03049-0/gif-abstract0/img3.gif) ( ).
References:
- 1.
- J.F. Adams, P.J. Hilton, On the chain algebra of a loop space, Comment. Math. Helvetici 30, (1956), pp. 305-330. MR 17:1119b
- 2.
- D.J. Anick, Hopf algebras up to homotopy, J. Amer. Math. Soc. 2, (1989), pp. 417-453. MR 90c:16007
- 3.
- A.K. Bousfield, Localization and periodicity in unstable homotopy theory, J. Amer. Math. Soc. 7, No.4 (1994), pp. 831-874. MR 95c:55010
- 4.
- A.K. Bousfield, D.M. Kan, Homotopy Limits, Completions, and Localizations, Springer Lecture Notes in Math. 304, (1972). MR 51:1825
- 5.
- W. Chachólski, Closed classes, Proc. Conf. on Algebraic Topology, Barcelona (1994), Progress in Math. Vol. 136, Birkhäuser (1996), pp. 95-118. MR 97e:55007
- 6.
- W. Chachólski, P.-E. Parent, and D. Stanley,
 -acyclic spaces versus  -cellular spaces, preprint. - 7.
- W. Chachólski, P.-E. Parent, and D. Stanley, Cellular generators, Proc. Amer. Math. Soc., To appear.
- 8.
- E. D. Farjoun, Cellular Spaces, Null Spaces and Homotopy Localization, Lecture Notes in Mathematics 1622 (1996). MR 98f:55010
- 9.
- Y. Félix, S. Halperin, and J.-C. Thomas, Rational homotopy theory, Graduate Texts in Mathematics 205, Springer-Verlag, (2001). MR 2002d:55014
- 10.
- S. Halperin, J.-M. Lemaire, Suites inertes dans les algèbres de Lie graduées, Math. Scand. 61, (1987), pp. 39-67. MR 89e:55022
- 11.
- K. Hess, The rational homotopy algebra and cellular type, preprint.
- 12.
- M.J. Hopkins, J.H. Smith, Nilpotence and stable homotopy theory II, Ann. of Math. 148, (1998), pp. 1-49. MR 99h:55009
- 13.
- D.W. Lewis, J.-P. Tignol, Classification theorems for central simple algebras with involution, Manuscripta Math. 100, (1999), pp. 259-276. MR 2000m:16027
- 14.
- A. Pfister, Quadratic forms with applications to algebraic geometry and topology, London Math. Soc., Lecture Note Series 217, Cambridge University Press, (1995). MR 97c:11046
- 15.
- D. Quillen, Rational homotopy theory, Annals of Math. (2) 90, (1969), pp. 205-295. MR 41:2678
- 16.
- W. Scharlau, Quadratic and hermitian forms, A series of comprehensive studies in mathematics 270, Springer-Verlag, (1985). MR 86k:11022
- 17.
- D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), pp. 269-331. MR 58:31119
- 18.
- D. Tanré, Homotopie Rationnelle: Modèles de Chen, Quillen, Sullivan, Lecture Notes in Math. 1025, Springer-Verlag, (1983). MR 86b:55010
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
11E04, 55P60, 55P62
Retrieve articles in all Journals with MSC
(2000):
11E04, 55P60, 55P62
Additional Information:
Kathryn
Hess
Affiliation:
Chaire d'Algèbre, Département de Mathématiques, Ecole Polytechnique Fédérale, 1015 Lausanne, Suisse
Email:
kathryn.hess@epfl.ch
Paul-Eugène
Parent
Affiliation:
Chaire d'Algèbre, Département de Mathématiques, Ecole Polytechnique Fédérale, 1015 Lausanne, Suisse
Email:
paul-eugene.parent@epfl.ch
DOI:
10.1090/S0002-9947-02-03049-0
PII:
S 0002-9947(02)03049-0
Keywords:
Cellular space,
quadratic form,
Witt group,
Quillen model
Received by editor(s):
November 6, 2001
Received by editor(s) in revised form:
March 19, 2002
Posted:
July 2, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org