PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1995 | 147 | 2 | 99-126
Tytuł artykułu

Self homotopy equivalences of classifying spaces of compact connected Lie groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We describe, for any compact connected Lie group G and any prime p, the monoid of self maps $BG_{^p}$ → $BG_{^p}$ which are rational equivalences. Here, $BG_{^p}$ denotes the p-adic completion of the classifying space of G. Among other things, we show that two such maps are homotopic if and only if they induce the same homomorphism in rational cohomology, if and only if their restrictions to the classifying space of the maximal torus of G are homotopic.
Słowa kluczowe
Rocznik
Tom
147
Numer
2
Strony
99-126
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-03-15
poprawiono
1994-10-05
Twórcy
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland, sjack@mimuw.edu.pl
  • Department of Mathematics, Purdue University, West Lafayette, Indiana 47909-1395, U.S.A., mcclure@math.purdue.edu
autor
Bibliografia
  • [Ad] J. F. Adams, Lectures on Lie Groups, Benjamin, 1969.
  • [AM] J. F. Adams and Z. Mahmud, Maps between classifying spaces, Invent. Math. 35 (1976), 1-41.
  • [Br] A. Borel, Topics in the Homology Theory of Fiber Bundles, Lecture Notes in Math. 36, Springer, 1967.
  • [Bt] R. Bott, On torsion in Lie groups, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 586-588.
  • [Bb1] N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4-6, Hermann 1968.
  • [Bb2] N. Bourbaki, Groupes et algèbres de Lie, Chapitre 9, Hermann, 1982.
  • [Bf] A. Bousfield, Homotopy spectral sequences and obstructions, Israel J. Math. 66 (1989), 54-104.
  • [BK] A. Bousfield and D. Kan, Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer, 1972.
  • [DW] W. Dwyer and C. Wilkerson, A new finite loop space at the prime two, J. Amer. Math. Soc. 6 (1993), 37-64.
  • [DW2] W. Dwyer and C. Wilkerson, The center of a p-compact group, in: The Čech Centennial: A Conference on Homotopy Theory, M. Cenkl and H. Miller (eds.), Contemp. Math. 181, Amer. Math. Soc., to appear.
  • [DZ] W. Dwyer and A. Zabrodsky, Maps between classifying spaces, in: Algebraic Topology, Barcelona, 1976, Lecture Notes in Math. 1298, Springer, 1987, 106-119.
  • [Fe] M. Feshbach, The Segal conjecture for compact Lie groups, Topology 26 (1987), 1-20.
  • [Fr] E. Friedlander, Exceptional isogenies and the classifying spaces of simple Lie groups, Ann. of Math. 101 (1975), 510-520.
  • [Hu] J. Hubbuck, Homotopy representations of Lie groups, in: New Developments in Topology, London Math. Soc. Lecture Note Ser. 11, Cambridge Univ. Press, 1974, 33-41.
  • [Is] K. Ishiguro, Unstable Adams operations on classifying spaces, Math. Proc. Cambridge Philos. Soc. 102 (1987), 71-75.
  • [JMO] S. Jackowski, J. McClure and B. Oliver, Homotopy classification of self-maps of BG via G-actions, Ann. of Math. 135 (1992), 183-270.
  • [Ml] J. Milnor, Morse Theory, Princeton Univ. Press, 1969.
  • [Ms] G. Mislin, The homotopy classification of self-maps of infinite quaternionic projective space, Quart. J. Math. Oxford 38 (1987), 245-257.
  • [MZ] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, 1955.
  • [Mø] J. M. Møller, The normalizer of the Weyl group, Math. Ann. 294 (1992), 59-80.
  • [No1] D. Notbohm, Maps between classifying spaces, Math. Z. 207 (1991), 153-168.
  • [No2] D. Notbohm, Maps between classifying spaces and applications, J. Pure Appl. Algebra 89 (1993), 273-294.
  • [Su] D. Sullivan, Geometric Topology, Part I: Localization, Periodicity and Galois Symmetry, Mimeographed notes, M.I.T., 1970.
  • [Wi] C. W. Wilkerson, Self-maps of classifying spaces, in: Localization in Group Theory and Homotopy Theory, Lecture Notes in Math. 418, Springer, 1974, 150-157.
  • [Wo] Z. Wojtkowiak, On maps from holim F to Z, in: Algebraic Topology, Barcelona, 1986, Lecture Notes in Math. 1298, Springer, 1987, 227-236.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv147i2p99bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.