When is a fourfold Massey product defined?

Isaksen, Daniel

doi:10.1090/S0002-9939-2014-12387-2

When is a fourfold Massey product defined?
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by Daniel C. Isaksen PDF

Proc. Amer. Math. Soc. 143 (2015), 2235-2239 Request permission

Abstract:

We define a new invariant in the homology of a differential graded algebra. This invariant is the obstruction to defining a fourfold Massey product. It can be used to detect differential graded algebras that are not quasi-isomorphic. We also make an explicit calculation in the cohomology of the Steenrod algebra.

References

M. G. Barratt, J. D. S. Jones, and M. E. Mahowald, Relations amongst Toda brackets and the Kervaire invariant in dimension $62$, J. London Math. Soc. (2) 30 (1984), no. 3, 533–550. MR 810962, DOI 10.1112/jlms/s2-30.3.533
M. G. Barratt, M. E. Mahowald, and M. C. Tangora, Some differentials in the Adams spectral sequence. II, Topology 9 (1970), 309–316. MR 266215, DOI 10.1016/0040-9383(70)90055-8
D. C. Isaksen, Motivic stable stems, preprint, 2014.
David Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966), 431–449. MR 202136, DOI 10.1090/S0002-9947-1966-0202136-1
W. S. Massey, Higher order linking numbers, J. Knot Theory Ramifications 7 (1998), no. 3, 393–414. MR 1625365, DOI 10.1142/S0218216598000206
J. Peter May, Matric Massey products, J. Algebra 12 (1969), 533–568. MR 238929, DOI 10.1016/0021-8693(69)90027-1
Mark Mahowald and Martin Tangora, Some differentials in the Adams spectral sequence, Topology 6 (1967), 349–369. MR 214072, DOI 10.1016/0040-9383(67)90023-7
R. Michael F. Moss, Secondary compositions and the Adams spectral sequence, Math. Z. 115 (1970), 283–310. MR 266216, DOI 10.1007/BF01129978