| Abstrakt: |
We will show that the singular cohomology groups of a smooth quasi-projective complex variety relative to a normal crossing divisor can be described in terms of δ-admissible chains. Roughly speaking, a δ-admissible chain is a simplicial semi-algebraic chain meeting the "faces" properly. As an application, we show that the Abel-Jacobi map for higher Chow cycles can be described via δ-admissible chains. As an example, we will describe the Hodge realization of the polylog cycles constructed by Bloch-Kriz in terms of the Abel-Jacobi map. [ABSTRACT FROM AUTHOR] |
