DOI QR코드

DOI QR Code

CHARACTERIZATION OF PHANTOM GROUPS

  • LEE, DAE-WOONG (Department of Mathematics Chonbuk National University)
  • Published : 2005.04.01

Abstract

We give another characteristic feature of the set of phantom maps: After constructing an isomorphism between derived functors, we show that the set of homotopy classes of phantom maps could be restated as the extension product of subinverse towers induced by the given inverse towers.

References

  1. A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304 (1972)
  2. D. Lee, Derived cup product and (strictly) derived groups, Bull. Korean Math. Soc. 35 (1998), no. 4, 791-807
  3. D. Lee, Derived cup product Phantom maps and the Gray index, Topology Appl. 138 (2004), no. 1-3, 265-275 https://doi.org/10.1016/j.topol.2003.02.001
  4. C. A. McGibbon, Phantom maps, Handbook of algebraic topology, North-Holland, New York, 1995
  5. C. A. McGibbon and J. Roitberg, Connected coverings, phantom maps and genus sets, Indiana Univ. Math. J. 47 (1998), no. 4, 1433-1458
  6. G. Nobeling, Uber die derivierten des inversen und des derekten limes einer modulfamilie, Topology 1 (1961), 47-61 https://doi.org/10.1016/0040-9383(62)90095-2
  7. J. Roitberg and P. Touhey, The homotopy fiber of profinite completion, Topology Appl. 103 (2000), 295-307 https://doi.org/10.1016/S0166-8641(99)00006-1