Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Ginzburg's bivariant Chern classes


Author: Shoji Yokura
Journal: Trans. Amer. Math. Soc. 355 (2003), 2501-2521
MSC (2000): Primary 14C17, 14F99, 55N35
Published electronically: February 6, 2003
MathSciNet review: 1974000
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The convolution product is an important tool in geometric representation theory. Ginzburg constructed the ``bivariant" Chern class operation from a certain convolution algebra of Lagrangian cycles to the convolution algebra of Borel-Moore homology. In this paper we prove a ``constructible function version" of one of Ginzburg's results; motivated by its proof, we introduce another bivariant algebraic homology theory $s\mathbb{AH} $ on smooth morphisms of nonsingular varieties and show that the Ginzburg bivariant Chern class is the unique Grothendieck transformation from the Fulton-MacPherson bivariant theory of constructible functions to this new bivariant algebraic homology theory, modulo a reasonable conjecture. Furthermore, taking a hint from this conjecture, we introduce another bivariant theory $\mathbb{GF} $ of constructible functions, and we show that the Ginzburg bivariant Chern class is the unique Grothendieck transformation from $\mathbb{GF} $ to $s\mathbb{AH} $satisfying the ``normalization condition" and that it becomes the Chern-Schwartz-MacPherson class when restricted to the morphisms to a point.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14C17, 14F99, 55N35

Retrieve articles in all journals with MSC (2000): 14C17, 14F99, 55N35


Additional Information

Shoji Yokura
Affiliation: Department of Mathematics and Computer Science, Faculty of Science, University of Kagoshima, 21-35 Korimoto 1-chome, Kagoshima 890-0065, Japan
Email: yokura@sci.kagoshima-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03252-5
PII: S 0002-9947(03)03252-5
Keywords: Bivariant theory; Chern-Schwartz-MacPherson class; Constructible function; Convolution
Received by editor(s): January 20, 2002
Published electronically: February 6, 2003
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (C) (No.\ 12640081), the Japanese Ministry of Education, Science, Sports and Culture
Article copyright: © Copyright 2003 American Mathematical Society