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Abstract: In 1981 W. Fulton and R. MacPherson introduced the notion of bivariant theoryBT, which is a sophisticated unification of covariant theories andcontravariant theories. This is for the study of singular spaces. In 2001 M.Levine and F. Morel introduced the notion of algebraic cobordism, which is auniversal 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, aspecial case of which is nothing but the oriented Borel-Moore functor withproducts. The present paper is a first one of the series to try to understandLevine-Morel-s algebraic cobordism from a bivariant-theoretical viewpoint, andits first step is to introduce OBT as a unification of BT and OBMF.

Autor: Shoji Yokura

Fuente: https://arxiv.org/

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