Terminology. The term single speed is understood to mean a single cog freewheel, which is illegal on the track, as are brakes which would be required to stop a single speed, unless you intend to drag your feet on the ground. Fixed gear is understood to mean a cog mounted directly to the hub w/o a freewheel, which permits stopping w/o brakes. This is important because the OP is clearly intending to ride a single freewheel with brakes, so the velodrome reference is irrelevant to the discussion.