Animals learn complex cognitive maps to navigate through physical environments or reason about abstract concepts. These maps are believed to be encoded by mammalian hippocampal grid and place cells, forming low-dimensional neural manifolds that support flexible navigation. However, beyond simple line and ring attractors, how the brain represents and navigates more complex neural manifolds remains unclear. In this study, we propose a solution for representing arbitrary nonlinear neural manifolds by approximating them with piecewise linear spaces composed of simplexes, known as “simplicial complexes.” Our circuit represents these simplicial complexes as stable attractors and supports navigation through coordinated control and planning. First, we derive the synaptic weights and plasticity rules needed to embed the dynamics of a simplex attractor and enable closed-loop feedback control for navigation within it. Next, we mathematically identify the conditions required to stitch simplex attractors together, forming a cohesive simplicial complex attractor. Specifically, two simplex attractors can be connected through sufficient mutual inhibition. Furthermore, we design a circuit that navigates across simplexes using shortest-path planning via recurrent dynamics on a hypergraph that encodes the connectivity between simplexes. Finally, we map our circuit to specific components in the navigation circuits of rodents and Drosophila, offering a plausible mechanism for goal-directed navigation in complex environments and generating experimental predictions for both systems.