Volume: 20, Issue: 10(2009)
pp. 1305-1334 DOI: 10.1142/S0129167X09005777
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Full Text (PDF, 367KB)
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| Title: |
ORIENTED BIVARIANT THEORIES, I |
| Author(s): |
SHOJI YOKURA
Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University, 21-35 Korimoto 1-chome, Kagoshima 890-0065, Japan
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| History: |
Received 26 April 2008
Revised 28 July 2008
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| Abstract: |
In 1981 W. Fulton and R. MacPherson introduced the notion of bivariant theory (BT), which is a sophisticated unification of covariant theories and contravariant theories. This is for the study of singular spaces. In 2001 M. Levine and F. Morel introduced the notion of algebraic cobordism, which is a universal oriented Borel–Moore functor with products (OBMF) of geometric type, in an attempt to understand better V. Voevodsky's (higher) algebraic cobordism. In this paper we introduce a notion of oriented bivariant theory (OBT), a special case of which is nothing but the oriented Borel–Moore functor with products. The present paper is a first one of the series to try to understand Levine–Morel's algebraic cobordism from a bivariant theoretical viewpoint, and its first step is to introduce OBT as a unification of BT and OBMF. |
| Keywords: |
Fulton–MacPherson's bivariant theory; (co)bordism; Chern classes; Grothendieck–Riemann–Roch; K-theory
AMSC numbers:
55N35, 55N22, 14C17, 14C40, 14F99, 19E99
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