Laser particle acceleration is examined from a topological viewpoint which analyses laser pulse irradiation on a thin foil target using two-dimensional particle-in-cell simulations. Laser ion acceleration schemes are classified by topology depending on whether the target after laser irradiation (deformed target) is homeomorphic to the initial target. When the deformed target is non-homeomorphic, high energy ions are generated with high efficiency, which is considerably influenced by the target thickness. However, when the deformed and initial targets are homeomorphic, the obtained ion energy is low and is less influenced by the target thickness.