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Hodge filtered complex bordism (1212.2173v3)
Published 10 Dec 2012 in math.AT, math.AG, and math.DG
Abstract: We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show that the theory satisfies a projective bundle formula and $\A1$-homotopy invariance. Moreover, we obtain transfer maps along projective morphisms.