Some examples of relations between non-stable integral cohomology operations
Bull. Korean Math. Soc. 2010 Vol. 47, No. 2, 275-286
Printed March 1, 2010
Andrew Percy
Monash University
Abstract : The algebraic structure of the natural integral cohomology operations is explored by means of examples. We decompose the generators of the groups $H^m(\mathbb{Z},n)$ with $2 \leq n \leq 7$ and $2 \leq m \leq 13$ 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.
Keywords : integral cohomology operation, relations
MSC numbers : 55S05
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