Mathematical Research Letters

Volume 15, Issue 1, January 2008 pp. 95-115.

Geometry of polysymbols

Authors: Masanori Morishita (1) and Yuji Terashima (2)
Author institution: Kyushu University (1) and Tokyo Institute of Technology (2)

Summary: We introduce a multiple generalization of the tame symbol, called {\em 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.

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