Without geospatial data management, today’s challenges in big data applications such as earth observation, geographic information system/building information modeling (GIS/BIM) integration, and 3D/4D city planning cannot be solved. Furthermore, geospatial data management plays a connecting role between data acquisition, data modelling, data visualization, and data analysis. It enables the continuous availability of geospatial data and the replicability of geospatial data analysis. In the first part of this article, five milestones of geospatial data management research are presented that were achieved during the last decade. The first one reflects advancements in BIM/GIS integration at data, process, and application levels. The second milestone presents theoretical progress by introducing topology as a key concept of geospatial data management. In the third milestone, 3D/4D geospatial data management is described as a key concept for city modelling, including subsurface models. Progress in modelling and visualization of massive geospatial features on web platforms is the fourth milestone which includes discrete global grid systems as an alternative geospatial reference framework. The intensive use of geosensor data sources is the fifth milestone which opens the way to parallel data storage platforms supporting data analysis on geosensors. In the second part of this article, five future directions of geospatial data management research are presented that have the potential to become key research fields of geospatial data management in the next decade. Geo-data science will have the task to extract knowledge from unstructured and structured geospatial data and to bridge the gap between modern information technology concepts and the geo-related sciences. Topology is presented as a powerful and general concept to analyze GIS and BIM data structures and spatial relations that will be of great importance in emerging applications such as smart cities and digital twins. Data-streaming libraries and “in-situ” geo-computing on objects executed directly on the sensors will revolutionize geo-information science and bridge geo-computing with geospatial data management. Advanced geospatial data visualization on web platforms will enable the representation of dynamically changing geospatial features or moving objects’ trajectories. Finally, geospatial data management will support big geospatial data analysis, and graph databases are expected to experience a revival on top of parallel and distributed data stores supporting big geospatial data analysis.

In order to perform topological queries on geographic data, it is necessary to first develop a topological access method (TOAM). Using the fact that any (incidence or other binary) relation produces a topology which includes the common usage of topology for spatial or spatiotemporal data, here, such a TOAM is developed on the basis of the previously applied concept of Property Graph used in order to manage topological information in data of any dimension, whether time dependent or not. As a matter of fact, it is necessary to have a TOAM in order to query such a graph, and also to have data which are topologically consistent in a certain sense. While the rendering of topological consistency was the concern of previous work, here, the aim is to develop a methodology which builds on this concept. In the end, an experimental test of this approach on a small city model is performed. It turned out that the Euler characteristic, a well-known topological invariant, can be helpful for the initial data validation. Practically, this present theoretical work is seen to be necessary in view of future innovative applications, e.g., in the context of city model simulations, including distributed geo-processing.

Geometrically induced topology plays a major role in applications such as simulations, navigation, spatial or spatio-temporal analysis and many more. This article computes geometrically induced topology useful for such applications and extends previous results by presenting the unpublished used algorithms to find inner disjoint $(d+1)$-dimensional simplicial complexes from a set of intersecting d-dimensional simplicial complexes which partly shape their B-Reps (Boundary Representations). CityGML has been chosen as the input data format for evaluation purposes. In this case, the input data consist of planar segment complexes whose triangulated polygons serve as the set of input triangle complexes for the computation of the tetrahedral model. The creation of the volumetric model and the computation of its geometrically induced topology is partly parallelized by decomposing the input data into smaller pices. A robustness analysis of the implementations is given by varying the angular precision and the positional precision of the epsilon heuristic inaccuracy model. The results are analysed spatially and topologically, summarised and presented. It turns out that one can extract most, but not all, volumes and that the numerical issues of computational geometry produce failures as well as a variety of outcomes.

Modern geo-data management plays a crucial role in designing digital twins in distributed system environments, enabling seamless integration, analysis, and visualization of spatial information. With the rise of graph databases and linked data, geospatial relationships can be efficiently modeled and queried using technologies such as Gremlin, a graph traversal language. On the other hand, Simple Features (see ISO19107) and the Dimensionally Extended 9-Intersection Model (DE-9IM) as two traditional examples provide standardized frameworks for spatial representation and topological reasoning, ensuring interoperability across systems. The fusion of geospatial standards with schema-free geo-data management advances the support of real-time decision-making and scalable geospatial applications, making modern geo-data management a cornerstone of intelligent, interconnected digital environments. Giving meaning to standards by ontologies is one major rapprochement to establish semantic interoperability. This paper provides one step towards this goal by using an abstract graph schema to represent the intra- and inter-relations of simplicial- and polytope-complexes and applying the traditional geoinformatics interpretation of topology, the philosophy of the Dimensionally Extended 9-Intersection Model (DE-9IM) to give meaning. This approach can be seen as a step towards the implementation of a Domain-Specific-Language (DSL) for property graphs that represent complex interrelated vector data within a linked data world.

Geometry and topology are both central concepts in geospatial data modelling and management. While geometry is the central concept for computational geometry applications, e.g. to intersect surfaces and solids in 3D space, topology is helpful for many application classes starting from city modelling to subsurface modelling and indoor navigation. Furthermore, p-adic numbers are useful for describing hierarchical processes on topological models. In this paper we first shortly review geometry- and topology-based approaches used for geospatial applications. We then describe our approach on turning geometry “upside down” focusing on topology during the whole process of distributed geospatial computing, data modelling, data management, and simulation. Furthermore, the way to use p-adic numbers for the description of hierarchical processes on topological models is shown for the example of simulation and the idea of p-adic analysis in distributed simulations is presented in the context of topological city and building models. The approach opens new insights such as topological relationships, components, and efficiently studying of the approximate behaviour of processes in the built environment using distributed computational systems. Finally, exemplary applications are presented to underline the importance of this new approach.