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Using Seibergs definition for the geometric charge in SU(2) lattice gauge theory, we have managed to apply it also to the Chern-Simons term. We checked the periodic structure and determined the Chern-Simons density on small lattices L 4 and L 3 × 2,4 with L = 4, 6, and 8 near the critcal region in the SU(2) Higgs mode. The data indicate that tunneling is increased at high temperature.