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1999 | 161 | 1-2 | 1-16
Tytuł artykułu

The normalizer splitting conjecture for p-compact groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group $W_X$. We prove that for an odd prime p, the fibration $BT → BN → BW_X$ has a section, which is unique up to vertical homotopy.
Rocznik
Tom
161
Numer
1-2
Strony
1-16
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-01-22
poprawiono
1998-07-04
Twórcy
  • Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 København Ø, Denmark, kksa@math.ku.dk
Bibliografia
  • [1] J. Aguadé, Constructing modular classifying spaces, Israel J. Math. 66 (1989), 23-40.
  • [2] D. J. Benson, Projective modules for the group of twenty-seven lines on a cubic surface, Comm. Algebra 17 (1989), 1017-1068.
  • [3] D. J. Benson, Polynomial Invariants of Finite Groups, London Math. Soc. Lecture Note Ser. 190, Cambridge Univ. Press, Cambridge, 1993.
  • [4] A. K. Bousfield and D. M. Kan, Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer, Berlin, 1987.
  • [5] C. Broto and A. Viruel, Homotopy uniqueness of BPU(3), in: Group Representations: Cohomology, Group Actions and Topology (Seattle, WA, 1996), Proc. Sympos. Pure Math. 63, Amer. Math. Soc., Providence, RI, 1998, 85-93.
  • [6] K. S. Brown, Cohomology of Groups, Grad. Texts in Math. 87, Springer, New York, 1994.
  • [7] J. Cannon and C. Playoust, An introduction to Magma, technical report, School of Math. and Statist., Univ. of Sydney, 1995.
  • [8] A. Clark and J. R. Ewing, The realization of polynomial algebras as cohomology rings, Pacific J. Math. 50 (1974), 425-434.
  • [9] A. M. Cohen, Finite complex reflection groups, Ann. Sci. École Norm. Sup. (4) 9 (1976), 379-436.
  • [10] H. M. S. Coxeter, Discrete groups generated by reflections, Ann. of Math. 35 (1934), 588-621.
  • [11] C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. I, Wiley, New York, 1990.
  • [12] M. Curtis, A. Wiederhold and B. Williams, Normalizers of maximal tori, in: P. Hilton (ed.), Localization in Group Theory and Homotopy Theory and Related Topics (Seattle, WA, 1974), Lecture Notes in Math. 418, Springer, Berlin, 1974, 31-47.
  • [13] W. G. Dwyer and C. W. Wilkerson, Homotopy fixed-point methods for Lie groups and finite loop spaces, Ann. of Math. (2) 139 (1994), 395-442.
  • [14] W. G. Dwyer and C. W. Wilkerson, The center of a p-compact group, in: M. Cenkl and H. Miller (eds.), The Čech Centennial (Boston, MA, 1993), Contemp. Math. 181, Amer. Math. Soc., Providence, RI, 1995, 119-157.
  • [15] W. G. Dwyer and C. W. Wilkerson, Product splittings for p-compact groups, Fund. Math. 147 (1995), 279-300.
  • [16] L. Evens, The Cohomology of Groups, Oxford Univ. Press, New York, 1991.
  • [17] R. B. Howlett, On the Schur multipliers of Coxeter groups, J. London Math. Soc. (2) 38 (1988), 263-276.
  • [18] J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Stud. Adv. Math. 29, Cambridge Univ. Press, Cambridge, 1992.
  • [19] S. Ihara and T. Yokonuma, On the second cohomology groups (Schur multipliers) of finite reflection groups, J. Fac. Sci. Univ. Tokyo Sect. I 11 (1965), 155-171.
  • [20] S. Jackowski, J. McClure and R. Oliver, Homotopy classification of self-maps of BG via G-actions. I, Ann. of Math. (2) 135 (1992), 183-226.
  • [21] J. Lannes, Théorie homotopique des groupes de Lie (d'après W. G. Dwyer et C. W. Wilkerson), Astérisque 227 (1995), 21-45.
  • [22] J. M. Møller, Homotopy Lie groups, Bull. Amer. Math. Soc. (N.S.) 32 (1995), 413-428.
  • [23] J. M. Møller, Deterministic p-compact groups, in: W. Dwyer et al. (eds.), Stable and Unstable Homotopy (Toronto, 1996), Fields Inst. Comm. 19, Amer. Math. Soc., Providence, RI, 1998, 255-278.
  • [24] J. M. Møller, Normalizers of maximal tori, Math. Z. 231 (1999), 51-74.
  • [25] J. M. Møller and D. Notbohm, Centers and finite coverings of finite loop spaces, J. Reine Angew. Math. 456 (1994), 99-133.
  • [26] M. Nakaoka, Decomposition theorems for homology groups of symmetric groups, Ann. Math. (2) 71 (1960), 16-42.
  • [27] D. Notbohm, Unstable splittings of classifying spaces of p-compact groups, preprint, 1994.
  • [28] D. Notbohm, Classifying spaces of compact Lie groups, in: I. M. James (ed.), Handbook of Algebraic Topology, North-Holland, Amsterdam, 1995, 1049-1094.
  • [29] D. Notbohm, On the "classifying space" functor for compact Lie groups, J. London Math. Soc. (2) 52 (1995), 185-198.
  • [30] D. Notbohm, p-adic lattices of pseudoreflection groups, in: C. Broto et al. (eds.), Algebraic Topology: New Trends in Localization and Periodicity (Sant Feliu de Guíxols, 1994), Progr. Math. 136, Birkhäuser, Basel, 1996, 337-352.
  • [31] E. W. Read, On the Schur multipliers of the finite imprimitive unitary reflection groups G(m,p,n), J. London Math. Soc. (2) 13 (1976), 150-154.
  • [32] H. Scheerer, Homotopieäquivalente kompakte Liesche Gruppen, Topology 7 (1968), 227-232.
  • [33] G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canad. J. Math. 6 (1954), 274-304.
  • [34] L. Smith, Polynomial Invariants of Finite Groups, Res. Notes in Math. 6, A K Peters, Wellesley, MA, 1995.
  • [35] J. Tits, Normalisateurs de tores I. Groupes de Coxeter étendus, J. Algebra 4 (1966), 96-116.
  • [36] R. van der Hout, The Schur multipliers of the finite primitive complex reflection groups, Nederl. Akad. Wetensch. Proc. Ser. A 80 = Indag. Math. 39 (1977), 101-113.
  • [37] C. A. Weibel, An Introduction to Homological Algebra, Cambridge Stud. Adv. Math. 38, Cambridge Univ. Press, Cambridge, 1994.
  • [38] G. W. Whitehead, Elements of Homotopy Theory, Grad. Texts in Math. 61, Springer, New York, 1978.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv161i1p1bwm
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