Subject: New Book: Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations From: Valerie J Yaw Date: Tue, 4 Oct 2005 15:52:44 -0400 Valerie Yaw Marketing Associate Cambridge University Press 40 West 20th Street New York, NY 10011-4211 telephone 212.337.5076 facsimile 212.691.3239 e-mail vyaw@cambridge.org Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations Dagmar M. Meyer and Larry Smith Poincaré duality algebras originated in the work of topologists on the cohomology of closed manifolds, and Macaulay's dual systems in the study of irreducible ideals in polynomial algebras. Steenrod operations also originated in algebraic topology and they provide a noncommutative tool to study commutative algebras over a Galois field. The authors skilfully bring together these ideas and apply them to problems in invariant theory. A number of remarkable and unexpected interdisciplinary connections are revealed that will interest researchers in the areas of commutative algebra, invariant theory or algebraic topology. Contents: Introduction; Part I. Poincaré Duality Quotients: Part II. Macaulay’s Dual Systems and Frobenius Powers: Part III. Poincaré Duality and the Steenrod Algebra: Part IV. Dickson, Symmetric, and Other Coinvariants: Part V. The Hit Problem mod 2: Part VI. Macaulay’s Inverse Systems and Applications: References; Notation; Index. $75.00 / September 2005 / 199 pages / Hardback / 0-521-85064-9 Series: Cambridge Tracts in Mathematics (No. 167) 5 line diagrams / 5 tables / 5 figures / 25 worked examples To order a copy, please visit www.cambridge.org/0521850649