Wolfgang Pitsch (Universitat Autònoma de Barcelona)
Witt group and Maslov index
Abstract: The main subjects of this talk will be $W(k)$, the Witt group over a field $k$, and the Maslov index of three Lagrangians in a symplectic space, which is an invariant, originally introduced in topology, taking values in $W(k)$. I will show how the machinery of Sturm sequences and Sylvester matrices developed by Barge-Lannes can be used to prove that the equivalence class of Maslov’s 2-cocycle, associated to the homonymous index, is trivial modulo $I^2$, with $I$ being the fundamental ideal of $W(k)$.