We introduce a multiple generalization of the tame symbol, called polysymbols, associated to meromorphic functions on a Riemann surface as the Massey products in Deligne cohomology, and also give a geometric construction of polysymbols using Chen's iterated integrals. We then deduce some basic properties of polysymbols using our holonomy formula, and show that trivializations of polysymbols give variations of mixed Hodge structure.
|Number of pages||21|
|Journal||Mathematical Research Letters|
|Publication status||Published - 2008 Jan|
- Deligne cohomology
- Iterated integral
- Massey product
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