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1999 | 162 | 3 | 209-232
Tytuł artykułu

Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P(n)-cohomology of DI(4). We use the non-commutativity of the spectrum P(n) at p=2 to prove the non-homotopy nilpotency of DI(4). Concerning the classifying space, we prove that the BP-cohomology and the Morava K-theories of BDI(4) are all concentrated in even degrees.
Słowa kluczowe
Rocznik
Tom
162
Numer
3
Strony
209-232
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-05-12
poprawiono
1999-08-18
Twórcy
autor
  • Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain, msantos@goliat.ugr.es
Bibliografia
  • [A-W] Adams, J. F. and Wilkerson, C. W., Finite H-spaces and algebras over the Steenrod algebra, Ann. of Math. 111 95-143 (1980).
  • [B] Bourbaki, N., Groupes et algèbres de Lie, Masson, Paris, 1981.
  • [D-W1] Dwyer, W. G. and Wilkerson, C. W., Homotopy fixed point methods for Lie groups and finite loop spaces, Ann. of Math. 139 395-442 (1994).
  • [D-W2] Dwyer, W. G. and Wilkerson, C. W., A new finite loop space at the prime two, J. Amer. Math. Soc. 6 37-64 (1993).
  • [Ho] Hopkins, M., Nilpotence and finite H-spaces, Israel J. Math. 66 (1989), 238-246.
  • [J-W] Johnson, D. C. and Wilson, W. S., BP operations and Morava's extraordinary K-theories, Math. Z. 144 55-75 (1975).
  • [K-Ya] Kono, A. and Yagita, N., Brown-Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups, Trans. Amer. Math. Soc. 339 781-798 (1993).
  • [R] Rao, V. K., Spin(n) is not homotopy nilpotent for n ≥ 7, Topology 32 (1993), 239-249.
  • [R-W-Ya] Ravenel, D. C., Wilson, W. S. and Yagita, N. , Brown-Peterson cohomology from Morava K-theory, K-theory, to appear.
  • [S-Ya] Shimada, N. and Yagita, N., Multiplications in complex bordism theory with singularities, Publ. Res. Inst. Math. Sci. Kyoto Univ. 12 259-293 (1976).
  • [S-S] Smith, L. and Switzer, R. M., Realizability and nonrealizability of Dickson algebras as cohomology rings, Proc. Amer. Math. Soc. 89 303-313 (1983).
  • [Wu1] Wurgler, U., Commutative ring-spectra of characteristic 2, Comment. Math. Helv. 61 33-45 (1986).
  • [Wu2] Wurgler, U., On products in a family of cohomology theories associated to the invariant prime ideals of $π_*(BP)$, ibid. 52 457-481 (1977).
  • [Ya1] Yagita, N., The exact functor theorem for $BP_*/I_n$-theory, Proc. Japan Acad. 52 1-3 (1976).
  • [Ya2] Yagita, N., On mod odd prime Brown-Peterson cohomology groups of exceptional Lie groups, J. Math. Soc. Japan 34 293-305 (1982).
  • [Ya3] Yagita, N., Homotopy nilpotency for simply connected Lie groups, Bull. London Math. Soc. 25 481-486 (1993).
  • [Ya4] Yagita, N., On the Steenrod algebra of Morava K-theory, J. London Math. Soc. 22 423-438 (1980).
  • [Z] Zabrodsky, A., Hopf Spaces, North-Holland Math. Stud. 22, North-Holland, Amsterdam, 1976.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv162i3p209bwm
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