RANSACTIONS SOCIETY MATHEMATICAL CAN OF THE WHOLE NUMBER 684 MAY 1992 VOLUME 331 NUMBER 1 EDITED BY

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1 MAY 1992 VOLUME 331 NUMBER 1 WHOLE NUMBER 684 RANSACTIONS OF THE CAN MATHEMATICAL SOCIETY EDITED BY Avner D. Ash James E. Baumgartner, Managing Editor Robert Bryant Sun-Yung A. Chang Ralph Cohen Richard Durrett Philip J. Hanlon David Jerison Wen-Ching Winnie Li John Mallet-Paret Judith D. Sally Peter Shalen Masamichi Takesaki PROVIDENCE, RHODE ISLAND USA ISSN

2 TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY THIS JOURNAL is devoted entirely to research in pure and applied mathematics, and includes, in general, longer papers than those in the PROCEEDINGS. Papers should be at least 16 typed pages in length. PREPARATION OF THE MANUSCRIPT. All papers should be typewritten double-spaced, and two copies should be sent to the appropriate editor. The author should keep a complete copy. To encourage the submission of manuscripts in electronic form using TrfX and the Ü7vlS-TrfX macro package, the Executive Committee of the Council has adopted a policy that allows for accelerating the publication date of such manuscripts by as much as 20 weeks, which is approximately equal to the time normally needed by the Society for copyediting, typesetting, and proofreading an average manuscript. FORM OF MANUSCRIPT. The first page should consist of a descriptive title, followed by an abstract which summarizes the article in language suitable for workers in the general field (algebra, analysis, etc.). The descriptive title should be short, but informative; useless or vague phrases such as "Some remarks about" or "concerning" should be avoided. Also avoid proper names unless mathematical usage associates them with the work. The abstract should be at least one complete sentence, and at most 300 words, with the upper limit primarily for longer papers. Included with the footnotes to your paper, but placed before the first footnote, there should be first the 1991 Mathematics Subject Classification representing the primary and secondary subjects of the article, which may be followed by a list of key words and phrases describing the subject matter of the article and taken from it. A list of the numbers may be found in the annual subject index of Mathematical Reviews, published with the December issue starting in SUBMISSION OF MANUSCRIPT. See the back of this journal. COPYRIGHT TRANSFER AGREEMENT. The signing of a Copyright Transfer Agreement is a requirement for publication. GALLEY PROOF. When a paper with more than one author has been accepted for publication, only one set of galley proof will be sent. Joint authors should, therefore, indicate on the original manuscript which of them should receive galley proof in the event that the manuscript is accepted for publication. BACKLOG. 100 pages. Two-thirds of the papers currently being accepted by the editors will be published in 18 months. SUBSCRIPTION INFORMATION. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY is published monthly. Subscription prices for Volumes (1992) are $842 list; $674 institutional member. A late charge of 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year. Subscribers outside the United States and India must pay a postage surcharge of $27; subscribers in India must pay a postage surcharge of $50. Expedited delivery to destinations in North America $38; elsewhere $127. BACK NUMBER INFORMATION. Back number prices per volume are: for Volumes , $113 list, $90 institutional members; for Volumes , $131 list, $105 institutional members; for Volumes , $161 list, $129 institutional members; for Volumes , $179 list, $143 institutional members; for Volumes , $191 list, $153 institutional members; for Volumes , $195 list, $156 institutional members; for Volumes , $197 list, $158 institutional members; for Volumes , $188 list, $150 institutional members; for Volumes , $205 list, $164 institutional members. Volumes 1-77 may be ordered from Johnson Reprint Corporation, 111 Fifth Avenue, New York, New York Back numbers may be purchased on microfilm or microfiche from University Microfilms International, 300 North Zeeb Road, Ann Arbor, Michigan Subscriptions and orders for publications of the American Mathematical Society should be addressed to American Mathematical Society, P. O. Box 1571, Annex Station, Providence, R. I All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, R. I TRANSACTIONS of the American Mathematical Society is published monthly by the American Mathematical Society at 201 Charles Street, Providence, R. I Second-class postage is paid at Providence, Rhode Island. Postmaster: Send address changes to TRANSACTIONS, American Mathematical Society, P. O. Box 6248, Providence, R. I Copyright 1992 American Mathematical Society. All rights reserved. Printed in the United States of America Information on Copying and Reprinting can be found at the back of this journal. The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and This publication was typeset using AmS -TpX, the American Mathematical Society's Tr»X macro system

3 MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY This bimonthly journal is devoted to research in pure and applied mathematics of much the same nature as appears in TRANSACTIONS. An issue consists of one or more separately bound research tracts for which the author(s) has provided reproduction copy. Prior to 1975 this was published as a monograph series. The editorial committee is identical with that for the TRANSACTIONS so that papers intended for publication in this series should be addressed to one of the editors. SUBMISSION OF MANUSCRIPT Two copies of mathematical papers intended for publication in the TRANSACTIONS or the MEMOIRS should be addressed to one of the editors. Subjects, and the editors associated with them, follow. Harmonic analysis, representation theory, and Lie theory to AVNER D. ASH, Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH Abstract analysis to MASAMICHI TAKESAKI, Department of Mathematics, University of California, Los Angeles, CA Real and harmonic analysis to DAVID JERISON, Department of Mathematics, Room 2-180, Massachusetts Institute of Technology, Cambridge, MA Algebra and algebraic geometry to JUDITH D. SALLY, Department of Mathematics, Northwestern University, Evanston, IL Geometric topology, hyperbolic geometry, infinite group theory, and general topology to PETER SHALEN, Department of Mathematics, University of Illinois, Chicago, IL Algebraic topology and differential topology to RALPH COHEN, Department of Mathematics, Stanford University, Stanford, CA Ordinary differential equations, partial differential equations, and applied mathematics to JOHN MALLET-PARET, Division of Applied Mathematics, Brown University, Providence, RI Global analysis and differential geometry to ROBERT BRYANT, Department of Mathematics, Duke University, Durham, NC Probability and statistics to RICHARD DURRETT, Department of Mathematics, Cornell University, Ithaca, NY Combinatorics and Lie theory to PHILIP J. HANLON, Department of Mathematics, University of Michigan, Ann Arbor, MI Logic, set theory, general topology, and universal algebra to JAMES E. BAUM- GARTNER, Department of Mathematics, Dartmouth College, Hanover, NH Algebraic number theory, analytic number theory, and automorphic forms to WEN- CHING WINNIE LI, Department of Mathematics, Pennsylvania State University, University Park, PA Complex analysis and nonlinear partial differential equations to SUN-YUNG A. CHANG, Department of Mathematics, University of California, Los Angeles, CA All other communications to the editors should be addressed to the Managing Editor, JAMES E. BAUMGARTNER, Department of Mathematics, Dartmouth College, Hanover, NH COPYING AND REPRINTING Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Manager of Editorial Services, American Mathematical Society, P.O. Box 6248, Providence, Rhode Island The appearance of the code on the first page of an article in this journal indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem, Massachusetts This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale.

4 (Continued from back cover) Two-dimensional Cremona groups acting on simplicial complexes By David Wright. 281 A Haar-type theory of best Lx -approximation with constraints By András Kroó and Darrell Schmidt. 301 Gauge invariant quantization on Riemannian manifolds By Liu Zhang-Ju and Qian Min. 321 On the /7-adic completions of nonnilpotent spaces By A. K. Bousfield. 335 Normal form and linearization for quasiperiodic systems By Shui-Nee Chow, Kening Lu and Yun-Qiu Shen. 361 Multipliers of families of Cauchy-Stieltjes transforms By R. A. Hibschweiler and T. H. MacGregor. 377 An asymptotic estimate for heights of algebraic subspaces By Jeffrey Lin Thunder. 395 A simplifed trace formula for Hecke operators for Yo(N) By Shepley L. Ross II. 425 Noetherian ring extensions with trace conditions By Robert B. Warfield, Jr. 449

5 TRANSACTIONS OF THE AMERICAN MATHEMATICALSOCIETY Contents Vol. 331, No. 1 May 1992 Whole No. 684 The strong maximal function on a nilpotent group By Michael Christ. 1 The transverse homoclinic dynamics and their bifurcations at nonhyperbolic fixed points By Bo Deng. 15 Tensor products and Grothendieck type inequalities of operators in Lpspaces By Bernd Carl and Andreas Defant. Stable splittings of the dual spectrum of the classifying space of a compact Lie group By Chun-Nip Lee Nests of subspaces in Banach space and their order types By Alvaro Arias and Jeff Farmer. The helical transform as a connection between ergodic theory and harmonic analysis By Idris Assani and Karl Petersen. Aisimple proof of the fundamental theorem of Kirby calculus on links By Ning Lu A Chern character in cyclic homology By Luca Quardo Zamboni. 157 The structure of rings in some varieties with definable principal congruences By G. E. Simons. 165 On the resolution of a curve lying on a smooth cubic surface in P3 By Salvatore Giuffrida and Renato Maggioni. On the genus of smooth 4-manifolds By Alberto Cavicchioli. A quasiregular analogue of a theorem of Hardy and Littlewood By Craig A. Nolder. An open collar theorem for 4-manifolds By Craig R. Guilbault. L'espace des pseudo-arcs d'une surface By Robert Cauty Frames associated with an abelian /-group By James J. Madden. 265 (Continued on inside back cover)