D. ArcaraDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112Yuan-Pin LeeDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112
We verify the Invariance Conjectures of tautological equations in genus two. In particular, a uniform derivation of all known genus two equations is given.
D. ArcaraDepartment of Mathematics, Saint Vincent College, Latrobe PA 15650Yuan-Pin LeeDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112
We prove that all monomials of κ-classes and ψ-classes are independent in $R^k(\ocM_{g,n})/R^k(\partial\ocM_{g,n})$ for all k≤[g/3]. We also give a simple argument for κ_l≠0 in $R^l(\ocM_g)$ for l≤g−2.
Yuan-Pin LeeDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112R. PandharipandeDepartment of Mathematics, Princeton University, Princeton, New Jersey, 08540
The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over the rationals) of the corresponding cobordism groups over Spec(C) for all dimensions of varieties and ranks of bundles. The basis consists of split bundles over products of projective spaces. Moreover, we prove the full theory for bundles on varieties is an extension of scalars of standard algebraic cobordism.