For Jane Summers, a Midwest transplant who made the move to Beverly Hills three years ago, the community has all of the markings of a big city. The lights. The glitz. The traffic. But for Summers, who arrived at the Greendoor on Robertson Boulevard for the Beverly Hills Police Department’s Coffee with a Cop event, her newly adopted hometown is more of a tight-knit community than she realized. “I love living here. It just feels like a small town in the middle of a big city,” Summers said. “I grew up in the Midwest and these types of events are…