A principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in the combinatorial sense). We express rational local formulas for all powers of the first Chern class in terms of expectations of the parities of the associated necklaces. This rational parity is a combinatorial isomorphism invariant of a triangulated circle bundle over a simplex, measuring the mixing by the triangulation of the circular graphs over vertices of the simplex. The goal of this note is to sketch the logic of deducing these formulas from Kontsevitch’s cyclic invariant connection form on metric polygons.
Original languageEnglish
Pages (from-to)304-327
Number of pages24
JournalJournal of Mathematical Sciences (United States)
Volume224
Issue number2
DOIs
StatePublished - 1 Jul 2017

ID: 126276893