The torsion index of a $p$-compact group
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- by Jaume Aguadé
- Proc. Amer. Math. Soc. 138 (2010), 4129-4136
- DOI: https://doi.org/10.1090/S0002-9939-2010-10391-X
- Published electronically: May 27, 2010
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Abstract:
We extend the theory of torsion indices of compact connected Lie groups to $p$-compact groups and compute these indices in all cases.References
- K. K. S. Andersen, J. Grodal, J. M. Møller, and A. Viruel, The classification of $p$-compact groups for $p$ odd, Ann. of Math. (2) 167 (2008), no. 1, 95–210. MR 2373153, DOI 10.4007/annals.2008.167.95
- Kasper K. S. Andersen and Jesper Grodal, The classification of 2-compact groups, J. Amer. Math. Soc. 22 (2009), no. 2, 387–436. MR 2476779, DOI 10.1090/S0894-0347-08-00623-1
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- D. J. Benson and Jay A. Wood, Integral invariants and cohomology of $B\textrm {Spin}(n)$, Topology 34 (1995), no. 1, 13–28. MR 1308487, DOI 10.1016/0040-9383(94)E0019-G
- François-Xavier Dehon and Jean Lannes, Sur les espaces fonctionnels dont la source est le classifiant d’un groupe de Lie compact commutatif, Inst. Hautes Études Sci. Publ. Math. 89 (1999), 127–177 (2000) (French, with English and French summaries). MR 1793415
- Michel Demazure, Invariants symétriques entiers des groupes de Weyl et torsion, Invent. Math. 21 (1973), 287–301 (French). MR 342522, DOI 10.1007/BF01418790
- W. G. Dwyer and C. W. Wilkerson, A new finite loop space at the prime two, J. Amer. Math. Soc. 6 (1993), no. 1, 37–64. MR 1161306, DOI 10.1090/S0894-0347-1993-1161306-9
- W. G. Dwyer and C. W. Wilkerson, Homotopy fixed-point methods for Lie groups and finite loop spaces, Ann. of Math. (2) 139 (1994), no. 2, 395–442. MR 1274096, DOI 10.2307/2946585
- Mark Feshbach, The image of $H^{\ast } (BG,\,\textbf {Z})$ in $H^{\ast } (BT,\,\textbf {Z})$ for $G$ a compact Lie group with maximal torus $T$, Topology 20 (1981), no. 1, 93–95. MR 592571, DOI 10.1016/0040-9383(81)90015-X
- A. Grothendieck, La torsion homologique et les sections rationnelles, in Anneaux de Chow et applications, Séminaire C. Chevalley, 1958, 2nd year, Secrétariat math., Paris, exp. 5.
- Dietrich Notbohm, On the 2-compact group $\textrm {DI}(4)$, J. Reine Angew. Math. 555 (2003), 163–185. MR 1956596, DOI 10.1515/crll.2003.010
- Akimou Osse and Ulrich Suter, Invariant theory and the $K$-theory of the Dwyer-Wilkerson space, Une dégustation topologique [Topological morsels]: homotopy theory in the Swiss Alps (Arolla, 1999) Contemp. Math., vol. 265, Amer. Math. Soc., Providence, RI, 2000, pp. 175–185. MR 1803957, DOI 10.1090/conm/265/04248
- Larry Smith, Polynomial invariants of finite groups, Research Notes in Mathematics, vol. 6, A K Peters, Ltd., Wellesley, MA, 1995. MR 1328644
- Jacques Tits, Sur les degrés des extensions de corps déployant les groupes algébriques simples, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), no. 11, 1131–1138 (French, with English and French summaries). MR 1194504
- Burt Totaro, The torsion index of the spin groups, Duke Math. J. 129 (2005), no. 2, 249–290. MR 2165543, DOI 10.1215/S0012-7094-05-12923-4
- Burt Totaro, The torsion index of $E_8$ and other groups, Duke Math. J. 129 (2005), no. 2, 219–248. MR 2165542, DOI 10.1215/S0012-7094-05-12922-2
Bibliographic Information
- Jaume Aguadé
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Cerda- nyola del Vallès, Spain
- Email: aguade@mat.uab.cat
- Received by editor(s): February 5, 2009
- Published electronically: May 27, 2010
- Additional Notes: The author is partially supported by grants MTM2007-61545 and SGR2005-00606.
- Communicated by: Brooke Shipley
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 4129-4136
- MSC (2010): Primary 55P35, 57T15
- DOI: https://doi.org/10.1090/S0002-9939-2010-10391-X
- MathSciNet review: 2679635