外层空间
Karen Vogtmann (born July 13, 1949, in Pittsburg, California) is an American mathematician working primarily in the area of geometric group theory. She is known for having introduced, in a 1986 paper with Marc Culler, an object now known as the Culler–Vogtmann Outer space. The Outer space is a free group analog of the Teichmüller space of a Riemann surface and is particularly useful in the study of the group of outer automorphisms of the free group on "n" generators, Out("F""n"). Vogtmann is a professor of mathematics at Cornell University and The University of Warwick.