SOME EXAMPLES OF RELATIONS BETWEEN NON-STABLE INTEGRAL COHOMOLOGY OPERATIONS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The algebraic structure of the natural integral cohomology operations is explored by means of examples. We decompose the generators of the groups Hm(Z, n) with 2 ≤ n ≤ 7 and 2 ≤ m ≤ 13 into the operations of cup products, cross-cap products and compositions. Examination of these decompositions and comparison with other possible generators demonstrates the existence of relations between integral operations that have withheld formulation. The calculated groups and generators are collected in a table for practical reference.
Abstract
The algebraic structure of the natural integral cohomology operations is explored by means of examples. We decompose the generators of the groups Hm(Z, n) with 2 ≤ n ≤ 7 and 2 ≤ m ≤ 13 into the operations of cup products, cross-cap products and compositions. Examination of these decompositions and comparison with other possible generators demonstrates the existence of relations between integral operations that have withheld formulation. The calculated groups and generators are collected in a table for practical reference.
참고문헌 (9)
- H. Cartan, "Sur les groupes d'Eilenberg-Mac Lane. Ⅱ", Proc. Nat. Acad. Sci. U. S. A., 40, pp.704~707 (1954)
- W. Dreckmann, "On the definition of Π-algebras", C. R. Acad. Sci. Paris Ser. I Math., 321(6), pp.767~772 (1995)
- S. Eilenberg, "On the groups H(Π, n). Ⅱ", Methods of computation. Ann. of Math., 60, pp.49~139 (1954)
- S. O. Kochman, "Integral cohomology operations, Current trends in algebraic topology, Part 1", pp.437~478 (1982), Amer. Math. Soc.
- J. P. May, "A general algebraic approach to Steenrod operations, The Steenrod Algebra and its Applications", Proc. Conf. to Celebrate N. E. Steenrod's Sixtieth Birthday, pp.153~231 (1970)
- J. McCleary, "User's Guide To Spectral Sequences" (1985), Publish or Perish, Inc.
- A. Percy, "An Eckmann-Hilton dual to the Π-algebras of homotopy theory", Illinois J. Math., 48(4), pp.1305~1320 (2004)
- N. Steenrod, "Cohomology operations, and obstructions to extending continuous functions", Advances in Math., 8, pp.371~416 (1972)
- H. Toda, "Composition Methods in Homotopy Groups of Spheres" (1962), Princeton University Press