The twisting index in semitoric systems

• DOI: 10.48550/arxiv.2309.16614
• Publication Date: 2023-01-01
• Authors: Jaume Alonso; Sonja Hohloch; Joseph W. Palmer
• Keywords: Topological index

Semitoric integrable systems were symplectically classified by Pelayo and Vu Ngoc in 2009-2011 terms of five invariants. Four these invariants already well-understood prior to the classification, but fifth invariant, so-called twisting index came as a surprise. Intuitively, encodes how structure neighborhood focus-focus fiber compares large-scale semitoric system it was originally defined comparing certain momentum maps. In first half present paper, we produce several new formulations which give rise dynamical, geometric, topological interpretations. More specifically, describe differences action variables, Taylor series, homology cycles. second compute invariant specific family with two singular points (the generalized coupled angular momenta), is time that has been computed for more than one point. Moreover, also series up order. Since other this computed, becomes third all are known, after spin oscillators momenta.