Lawrence police announced Wednesday they are investigating three possible sex crimes – one involving a child.Police are investigating that sometime since the first of the year, a 43-year-old Lawrence man inappropriately touched a 15-year-old girl at the victim’s home. The incident was reported to police last week, and police wouldn’t release any further details.Police are also investigating an alleged rape early Saturday morning in southwest Lawrence. The 26-year-old female victim reported that a 29-year-old Lawrence man – an acquaintance of a friend – raped her at the home of another friend.In another incident, a man allegedly exposed himself to a woman Feb. 6 while both were walking along the 800 block of West Fourth Street. According to a police report, the woman was walking along the street a half-block behind the man, when the man turned and began walking towards her.The victim said the man asked her for the time, then opened his clothes to expose his body. The man, who has not yet been located, was described as a white male wearing black plastic pants with white stripes and a long gray T-shirt.