Fix an arbitrary prime p. Let F be a field containing a primitive p-th root of unity, with absolute Galois group GF, and let Hn denote its mod p cohomology group Hn(GF,Z/pZ). The triple Massey product (abbreviated 3MP) of weight (n,k,m)∈N3 is a partially defined, multi-valued function 〈⋅,⋅,⋅〉:Hn×Hk×Hm→Hn+k+m−1. In this work we prove that for an odd prime p, any defined 3MP of weight (1,k,1) contains zero.
Bibliographical noteFunding Information:
The author would like to thank I. Efrat for many interesting discussions and helpful suggestions, in particular for encouraging him to add the last part of the work avoiding the use of Kraines . The author would also like to thank the anonymous referee for many interesting comments and suggestions. This research was supported by the Israel Science Foundation (grant No. 630/17).
© 2017 Elsevier Inc.
- External cohomological operations
- Galois cohomology
- Massey products