Title: Lambda algebra unstable composition products and the
Lambda EHP sequence
Author: William Richter
AMS Classification numbers: 55T15, 55Q40, 55Q25
Address: Math Department, Northwestern University, Evanston IL 6020
Email: richter@math.nwu.edu
Abstract:
Simple combinatorial proofs are given of Lambda algebra results,
mostly due to Priddy & the 6 authors, but also the ``Adams filtration
better'' unstable Lambda products of Wang, Mahowald and Singer:
Lambda^{s,t}(n) @ Lambda(n+t ) ---> Lambda(n)
which imply the folklore Lambda EHP sequence
Lambda(n) >-E--> Lambda(n+1) -H-->> Lambda(2n+1)
The 6 authors proved Lambda(n) is a chain complex, but not that H is a
chain map. A careful reader could deduce a proof from the papers of
Wang, Mahowald and Singer, but Singer, who best stated the formulas,
gave no proofs. New results: combinatorial proofs of the Lambda
admissible monomial basis; the differential d is well-defined.
The paper should be accessible to geometers interested in forthcoming
applications with Mahowald on 3-cell Poincare complexes. Perhaps the
Lambda algebra is undergoing a Renaissance, as 2 young people, Mark
Behrens and Mizuho Hikida are doing interesting new work in it.