The module of indecomposables for finite 𝐻-spaces

Kane, Richard

doi:10.1090/S0002-9947-1976-0423341-1

The module of indecomposables for finite $H$-spaces
HTML articles powered by AMS MathViewer

by Richard Kane PDF

Trans. Amer. Math. Soc. 222 (1976), 303-318 Request permission

Abstract:

The module of indecomposables obtained from the $\bmod p$ cohomology of a finite H-space is studied for p odd. General structure theorems are obtained, first, regarding the possible even dimensions in which this module can be nonzero and, secondly, regarding how the Steenrod algebra acts on the module.

References

William Browder, Torsion in $H$-spaces, Ann. of Math. (2) 74 (1961), 24–51. MR 124891, DOI 10.2307/1970305
William Browder, On differential Hopf algebras, Trans. Amer. Math. Soc. 107 (1963), 153–176. MR 145530, DOI 10.1090/S0002-9947-1963-0145530-7
John Harper and Claude Schochet, Coalgebra extensions in two-stage Postnikov systems, Math. Scand. 29 (1971), 232–236 (1972). MR 310887, DOI 10.7146/math.scand.a-11048
John R. Harper, On the cohomology of stable two stage Postnikov systems, Trans. Amer. Math. Soc. 152 (1970), 375–388. MR 268892, DOI 10.1090/S0002-9947-1970-0268892-2
Richard Kane, On loop spaces without $p$ torsion, Pacific J. Math. 60 (1975), no. 1, 189–201. MR 383396, DOI 10.2140/pjm.1975.60.189
Richard Kane, Primitivity and finite $H$-spaces, Quart. J. Math. Oxford Ser. (2) 26 (1975), 309–313. MR 388383, DOI 10.1093/qmath/26.1.309
John Milnor, The Steenrod algebra and its dual, Ann. of Math. (2) 67 (1958), 150–171. MR 99653, DOI 10.2307/1969932
John W. Milnor and John C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211–264. MR 174052, DOI 10.2307/1970615
Alexander Zabrodsky, Secondary operations in the cohomology of $H$-spaces, Illinois J. Math. 15 (1971), 648–655. MR 322873

Secondary cohomology operations in the module of indecomposables