Acta Mathematica

Fixed point free actions on Z-acyclic 2-complexes

Bob Oliver and Yoav Segev

Full-text: Open access

Note

The first author was partially supported by the UMR 7539 of the CNRS, while the second author was partially supported by BSF Grant 97-00042 and by Grant 6782-1-95 from the Israeli Ministry of Science and Art.

Article information

Source
Acta Math., Volume 189, Number 2 (2002), 203-285.

Dates
Received: 6 September 2000
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891524

Digital Object Identifier
doi:10.1007/BF02392843

Mathematical Reviews number (MathSciNet)
MR1961198

Zentralblatt MATH identifier
1034.57033

Rights
2002 © Institut Mittag-Leffler

Citation

Oliver, Bob; Segev, Yoav. Fixed point free actions on Z -acyclic 2-complexes. Acta Math. 189 (2002), no. 2, 203--285. doi:10.1007/BF02392843. https://projecteuclid.org/euclid.acta/1485891524


Export citation

References

  • [A1] Aschbacher, M., Finite Group Theory. Cambrige Stud. Adv. Math., 10. Cambridge Univ. Press, Cambridge, 1986.
  • [A2] —, Overgroups of Sylow Subgroups in Sporadic Groups. Mem. Amer. Math. Soc., 60 (343). Amer. Math. Soc., Providence, RI, 1986.
  • [A3] —Sporadic Groups. Cambridge Tracts in Math., 104. Cambridge Univ. Press, Cambridge, 1994.
  • [AS] Aschbacher, M. & Segev, Y., A fixed point theorem for groups acting on finite 2-dimensional acyclic simplicial complexes. Proc. London Math. Soc. (3), 67 (1993), 329–354.
  • [At] Artin, E., Geometric Algebra. Reprint of the 1957 original, Wiley Classics Library. Wiley, New York, 1988.
  • [Bl] Bloom, D. M., The subgroups of PSL (3, q) for odd q. Trans. Amer. Math. Soc., 127 (1967), 150–178.
  • [Br] Bredon, G., Introduction to Compact Transformation Groups. Pure Appl. Math., 46. Academic Press, New York-London, 1972.
  • [Ca] Carter, R. W., Simple Groups of Lie Type. Pure Appl. Math., 28. Wiley, London-New York-Sydney, 1972.
  • [CC] Conway, J., Curtis, R., Norton, S., Parker, R. & Wilson, R., Atlas of Finite Groups. Oxford Univ. Press, Eynsham, 1985.
  • [FR] Floyd, E. E. & Richardson, R. W., An action of a finite group on an n-cell without stationary points. Bull. Amer. Math. Soc., 65 (1959), 73–76.
  • [G] Gorenstein, D., Finite Groups. Harper & Row, New York-London, 1968.
  • [GLS] Gorenstein, D., Lyons, R. & Solomon, R., The Classification of the Finite Simple Groups, Number 3, Part I, Chapter A. Almost Simple K-groups. Math. Surveys Monographs, 40.3. Amer. Math. Soc., Providence, RI, 1998.
  • [Gra] Gray, B., Homotopy Theory. Pure Appl. Math., 64. Academic Press, New York-London, 1975.
  • [Gri] Griess, R. L., Jr., Twelve Sporadic Groups. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 1998.
  • [H1] Huppert, B., Endliche Gruppen, I. Grundlehren Math. Wiss., 134. Springer-Verlag, Berlin, 1967.
  • [H2] Huppert, B. & Blackburn, N., Finite Groups, II. Grundlehren Math. Wiss., 242. Springer-Verlag, Berlin-New York, 1982.
  • [H3] —, Finite Groups, III. Grundlehren Math. Wiss., 243. Springer-Verlag, Berlin-New York, 1982.
  • [Ha] Hartley, R. W., Determination of the ternary collineation groups whose coefficients lie in the GF (2n). Ann. of Math. (2), 27 (1925), 140–158.
  • [Hu] Hu, S.-T., Homotopy Theory. Pure Appl. Math., 8. Academic Press, New York-London, 1959.
  • [Jac] Jacobinski, H., Genera and decompositions of lattices over orders. Acta Math., 121 (1968), 1–29.
  • [Jan] Janko, Z., A characterization of the smallest group of Ree associated with the simple Lie algebra of type (G2). J. Algebra, 4 (1966), 293–299.
  • [Kl1] Kleidman, P. B., Ph. D. thesis, Imperial College, London, 1987.
  • [Kl2] — The maximal subgroups of the Chevalley groups G2 (q) with q odd, the Ree groups2G2 (q), and their automorphism groups. J. Algebra, 117 (1988), 30–71.
  • [KS] Kirby, R. & Scharlemann, M., Eight faces of the Poincaré homology 3-sphere, in Geometric Topology (Athens, GA, 1977), pp. 113–146. Academic Press, New York-London, 1979.
  • [LW] Lundell, A. T. & Weingram, S., The Topology of CW Complexes. Van Nostrand Reinhold, New York, 1969.
  • [Ma] Mathieu, E., Sur la fonction cinq fois transitive de 24 quantités. J. Math. Pures Appl. (2), 18 (1873), 25–46.
  • [O1] Oliver, R., Fixed-point sets of group actions on finite acyclic complexes. Comment. Math. Helv., 50 (1975), 155–177.
  • [O2] — Smooth compact Lie group actions on disks. Math. Z., 149 (1976), 79–96.
  • [O3] — A proof of the Conner conjecture. Ann. of Math. (2), 103 (1976), 637–644.
  • [On] Ono, T., An identification of Suzuki groups with groups of generalized Lie type. Ann. of Math. (2), 75 (1962), 251–259; Corrigendum. Ibid., 77 (1963), 413.
  • [Q1] Quillen, D., Higher algebraic K-Theory, I, in Algebraic K-theory, I: Higher K-theories (Seattle, WA, 1972), pp. 85–147. Lecture Notes in Math., 341. Springer-Verlag, Berlin, 1973.
  • [Q2] —, Homotopy properties of the poset of nontrivial p-subgroups of a group. Adv. in Math., 28 (1978), 101–128.
  • [Re] Reiner, I., Maximal Orders. London Math. Soc. Monographs, 5. Academic Press, London-New York, 1975.
  • [Ri] Rim, D. S., Modules over finite groups. Ann. of Math. (2), 69 (1959), 700–712.
  • [S1] Segev, Y., Group actions on finite acyclic simplicial complexes. Israel J. Math., 82 (1993), 381–394.
  • [S2] —, Some remarks on finite 1-acyclic and collapsible complexes. J. Combin. Theory Ser. A, 65 (1994), 137–150.
  • [Se] Serre, J.-P., Trees. Springer-Verlag, Berlin-New York, 1980.
  • [St1] Steinberg, R., Lectures on Chevalley Groups. Notes prepared by John Faulkner and Robert Wilson. Yale University, New Haven, CT, 1968.
  • [St2] —, Endomorphisms of Linear Algebraic Groups. Mem. Amer. Math. Soc., 80. Amer. Math. Soc., Providence, RI, 1968.
  • [Su1] Suzuki, M., On a class of doubly transitive groups. Ann. of Math. (2), 75 (1962), 105–145.
  • [Su2] —, Group Theory, I. Grundlehren Math. Wiss., 247. Springer-Verlag, Berlin-New York, 1982.
  • [Sw] Swan, R. G., Induced representations and projective modules. Ann. of Math. (2), 71 (1960), 552–578.
  • [Wh] Whitehead, J. H. C., Combinatorial homotopy, I. Bull. Amer. Math. Soc., 55 (1949), 213–245.
  • [Wi] Witt, E., Die 5-fach transitiven Gruppen von Mathieu. Abh. Math. Sem. Hansischen Univ., 12 (1938), 256–264.