Abstract Topological simpliﬁcation is effective for analysis and visualisation of scalar data. However, topological simpliﬁ-cationofmultivariatedataislesswelldeveloped. Wedescribe multi-ﬁeldtopology simpliﬁcationstrategybasedonthe Reeb Space. We generalise critical nodes in the Reeb Graph to the Jacobi Structure of the Reeb Space that di-vides itintoregions. Thedual graph for these regions, the ReebSkeleton, has properties similartothe Reebgraph,and can be simpliﬁed using importance measures based on generalising persistence to Measure Persistence. Categories and Subject Descriptors (according to ACM CCS) : I.3.6 [Computer Graphics]: Methodology andTechniques—Graphics data structures and data types1. ContextScientiﬁc data is complex in nature and difﬁcult to vi-sualise. Topological tools have therefore become impor-tant in scientiﬁc visualisation, especially for scalar ﬁelds[CSvdP10,TP12]. Multivariate topology has been based onJacobi sets - a generalisation of critical points to multi-ﬁelds [EH04,BBD
['Amit Chattopadhyay', 'Hamish Carr', 'David J. Duke', 'Zhao Geng']
Simplifying Multivariate Topology (Extended Abstract)