nLab Lambda-algebra

Idea

What is called the Lambda algebra ($\Lambda$-algebra) in stable homotopy theory is a differential graded algebra over $\mathbb{F}_2$ whose chain homology is the second page of the classical Adams spectral sequence.

It has the advantage over the May spectral sequence that it tends to make the extension problem for the Adams spectral sequence more tractable (Kochman 96, corollary 5.2.8)

Related concepts

• EHP spectral sequence

• Curtis algorithm

References

The construction originates in

• Aldridge Bousfield, Edward Curtis, Daniel Kan, Daniel Quillen, D.L. Rector, J.W. Schlesinger, The mod-$p$ lower central series and the Adams spectral sequence, Topology, Volume 5, Issue 4, November 1966, Pages 331-342

See also

• Edward Curtis, The Dyer-Lashof algebra and the $\Lambda$-algebra, Illinois J. Math. Volume 19, Issue 2 (1975), 231-246. (Euclid)

Textbook accounts include

• Doug Ravenel, section 3.3 of Complex cobordism and stable homotopy groups of spheres 1986/2003

• Stanley Kochman, section 5.2 of Bordism, Stable Homotopy and Adams Spectral Sequences, AMS 1996