Symplectic geometry and topology of spatial polygons in Euclidean and Minkowski spaces

Abstract

In this work, we studied the relations between spatial polygons in Euclidean spaces and point configurations in projective line P'. We classi- (i('d all non-singular hexagon spa.ces and modified some methods to evaluate ( 'how(cohomology) rings of'pol3^gon spaces. In addition, we detoi-mine the Fano Hexagon spa.ces. Besides these algeliraic a.nd algebraic topological properties, we aiso gave explicit geometric structures to non-singular polygon spaces and examined their .syrnplectic geornetricai properties. We adapt(>d some previously known results for poly^gons in Euclidean space to polygons in .Vlinkowski space and esta.blished explicit catlculational tobis which are used in showing the integrability of the almost complex structure of moduli spaces of spatial polyygons.