Quasi-projective and relative cohomological dimension of groups
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- by Juan M. Alonso
- Trans. Amer. Math. Soc. 325 (1991), 715-739
- DOI: https://doi.org/10.1090/S0002-9947-1991-0991957-8
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Abstract:
We give a geometric interpretation of the quasi-projective dimension of groups, a notion introduced by Howie and Schneebeli [H-S1] as a generalization of the Identity Property.References
- Robert Bieri and Beno Eckmann, Relative homology and Poincaré duality for group pairs, J. Pure Appl. Algebra 13 (1978), no. 3, 277–319. MR 509165, DOI 10.1016/0022-4049(78)90012-9
- Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York-Berlin, 1982. MR 672956
- I. M. Chiswell, Exact sequences associated with a graph of groups, J. Pure Appl. Algebra 8 (1976), no. 1, 63–74. MR 399296, DOI 10.1016/0022-4049(76)90023-2
- Warren Dicks, Groups, trees and projective modules, Lecture Notes in Mathematics, vol. 790, Springer, Berlin, 1980. MR 584790
- M. J. Dunwoody, Accessibility and groups of cohomological dimension one, Proc. London Math. Soc. (3) 38 (1979), no. 2, 193–215. MR 531159, DOI 10.1112/plms/s3-38.2.193
- James Howie and Hans Rudolf Schneebeli, Groups of finite quasiprojective dimension, Comment. Math. Helv. 54 (1979), no. 4, 615–628. MR 552680, DOI 10.1007/BF02566296
- James Howie and Hans Rudolf Schneebeli, Cellular actions and groups of finite quasiprojective dimension, Math. Z. 170 (1980), no. 1, 85–90. MR 558890, DOI 10.1007/BF01214714
- Johannes Huebschmann, Cohomology theory of aspherical groups and of small cancellation groups, J. Pure Appl. Algebra 14 (1979), no. 2, 137–143. MR 524183, DOI 10.1016/0022-4049(79)90003-3
- Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504
- Richard G. Swan, Periodic resolutions for finite groups, Ann. of Math. (2) 72 (1960), 267–291. MR 124895, DOI 10.2307/1970135
- Richard G. Swan, Groups of cohomological dimension one, J. Algebra 12 (1969), 585–610. MR 240177, DOI 10.1016/0021-8693(69)90030-1
- Peter Scott and Terry Wall, Topological methods in group theory, Homological group theory (Proc. Sympos., Durham, 1977) London Math. Soc. Lecture Note Ser., vol. 36, Cambridge Univ. Press, Cambridge-New York, 1979, pp. 137–203. MR 564422
- Olympia Talelli, On cohomological periodicity for infinite groups, Comment. Math. Helv. 55 (1980), no. 2, 178–192. MR 576600, DOI 10.1007/BF02566680
- C. T. C. Wall, Pairs of relative cohomological dimension one, J. Pure Appl. Algebra 1 (1971), no. 2, 141–154. MR 322881, DOI 10.1016/0022-4049(71)90014-4 —, (Ed.), Homological group theory, London Math. Soc. Lecture Note Series 36, Cambridge University Press, Cambridge, 1979.
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 325 (1991), 715-739
- MSC: Primary 20J05; Secondary 57M05
- DOI: https://doi.org/10.1090/S0002-9947-1991-0991957-8
- MathSciNet review: 991957