Poincare Duality Algebras, Macaulays Dual Systems, And Steenrod Operations

CAMBRIDGE TRACTS IN MATHEMATICS General Editors B. BOLLOBAS, W. FULTON, A. KATOK, F. KIRWAN, P. SARNAK, B. SIMON Poincar´e Duality Algebras, Macaulay’s Dual Systems, and Steenrod Operations Poincar´e Duality Algebras, Macaulay’s Dual Systems, and Steenrod Operations DAGMAR M. MEYER AND LARRY SMITH cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521850643 © Cambridge University Press 2005 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2005 isbn-13 isbn-10 978-0-511-13042-7 eBook (NetLibrary) 0-511-13042-2 eBook (NetLibrary) isbn-13 isbn-10 978-0-521-85064-3 hardback 0-521-85064-9 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Introduction 1 Part I. Poincar´ e duality quotients 9 I.1 Poincar´e duality, Gorenstein algebras, and irreducible ideals . 9 I.2 Properties of irreducible ideals . . . . . . . . . . . . . . . . . . . . . . . . 14 I.3 The ancestor ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 I.4 Fundamental classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 I.5