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Algebra i Analiz, 2007 Volume 19, Issue 5, Pages 179–213 (Mi aa141)
Research Papers

Traces in oriented homology theories of algebraic varieties

K. I. Pimenov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: This paper is an attempt to axiomatize the notion of oriented homology theory. Under the axioms in question, a Chern structure determines an orientation and vice versa. The main result of the paper is the projective bundle theorem in § 2.

Keywords: Chern class, Thom isomorphism, orientation, homology theory.

MSC: 4F43

Received: 10.04.2007


 English version: St. Petersburg Mathematical Journal, 2008, 19:5, 805–828

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© Steklov Math. Inst. of RAS, 2025