Vol. 9, No. 6, 2015

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Bivariant algebraic cobordism

José Luis González and Kalle Karu

Vol. 9 (2015), No. 6, 1293–1336

We associate a bivariant theory to any suitable oriented Borel–Moore homology theory on the category of algebraic schemes or the category of algebraic G-schemes. Applying this to the theory of algebraic cobordism yields operational cobordism rings and operational G-equivariant cobordism rings associated to all schemes in these categories. In the case of toric varieties, the operational T-equivariant cobordism ring may be described as the ring of piecewise graded power series on the fan with coefficients in the Lazard ring.

algebraic cobordism, bivariant and operational theories, operational (equivariant) cobordism, operational equivariant cobordism of toric varieties
Mathematical Subject Classification 2010
Primary: 14C17
Secondary: 14C15, 14F43, 14M25, 55N22, 57R85
Received: 28 January 2013
Revised: 21 April 2015
Accepted: 20 May 2015
Published: 7 September 2015
José Luis González
Department of Mathematics
Yale University
10 Hillhouse Avenue
New Haven, CT 06511
United States
Kalle Karu
Department of Mathematics
University of British Columbia
1984 Mathematics Road
Vancouver, BC V6T 1Z2