Collectives are often able to process information in a distributed fashion, surpassing each individual member's processing capacity. In fission-fusion dynamics, where group members come together and split from others often, sharing complementary information about uniquely known foraging areas could allow a group to track a heterogenous foraging environment better than any group member on its own. We analyse the partial overlaps between individual spider monkey core ranges, which we assume represent the knowledge of an individual during a given season. Sets of individuals with complementary overlaps are identified, showing a balance between redundantly and uniquely known portions, and we use simplicial complexes to represent these higher-order interactions. The structure of the simplicial complexes shows holes in various dimensions, revealing complementarity in the foraging information that is being shared. We propose that the complex spatial networks arising from fission-fusion dynamics allow for adaptive, collective processing of foraging information in dynamic environments.