Mathematical Research Letters

Volume 15 (2008)

Number 1

Geometry of polysymbols

Pages: 95 – 115



Masanori Morishita (Kyushu University)

Yuji Terashima (Tokyo Institute of Technology)


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.

Published 1 January 2008