Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The module of indecomposables for finite $ H$-spaces


Author: Richard Kane
Journal: Trans. Amer. Math. Soc. 222 (1976), 303-318
MSC: Primary 55D45; Secondary 57F05
DOI: https://doi.org/10.1090/S0002-9947-1976-0423341-1
MathSciNet review: 0423341
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] W. Browder, Torsion in H-spaces, Ann. of Math. (2) 74 (1961), 24-51. MR 23 #A2201. MR 0124891 (23:A2201)
  • [2] -, On differential Hopf algebras, Trans. Amer. Math. Soc. 108 (1963), 153-176. MR 26 #3061. MR 0145530 (26:3061)
  • [3] J. Harper and C. Schochet, Coalgebra extensions in two stage Postinikov systems, Math. Scand. 29 (1971), 232-236. MR 46 #9985. MR 0310887 (46:9985)
  • [4] J. Harper, On the cohomology of stable two stage Postnikov systems, Trans. Amer. Math. Soc. 152 (1970), 375-388. MR 42 #3789. MR 0268892 (42:3789)
  • [5] R. Kane, On loop spaces without p torsion, Pacific J. Math. 60 (1975), 189-201. MR 0383396 (52:4277)
  • [6] -, Primitivity and finite H-spaces, Oxford Quart. 26 (1975), 309-313. MR 0388383 (52:9220)
  • [7] J. Milnor, The Steenrod algebra and its dual, Ann. of Math. (2) 67 (1958), 150-171. MR 20 #6092. MR 0099653 (20:6092)
  • [8] J. Milnor and J. C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211-264. MR 30 #4259. MR 0174052 (30:4259)
  • [9] A. Zabrodsky, Secondary operations in the cohomology of H-spaces, Illinois J. Math. 15 (1971), 648-655. MR 48 #1234. MR 0322873 (48:1234)
  • [10] -, Secondary cohomology operations in the module of indecomposables, Algebraic Topology Conference, Aarhus, 1970.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55D45, 57F05

Retrieve articles in all journals with MSC: 55D45, 57F05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0423341-1
Keywords: H-space, $ \bmod\;p$ finite, Hopf algebra, indecomposable, primitive, Steenrod algebra, secondary operation
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society