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branched surface
In mathematics, a branched surface is a generazliation of both surfaces and train tracks.
==Definition==
A surface is a space that looks topologically (i.e., up to homeomorphism) like ℝ².
Consider, however, the space obtained by taking the quotient of two copies A,B of ℝ² under the identification of a closed half-space of each with a closed half-space of the other. This will be a surface except along a single line. Now, pick another copy C of ℝ and glue it and A together along halfspaces so that the singular line of this gluing is transverse in A to the previous singular line.
Call this complicated space K. A branched surface is a space that is locally modeled on K.〔Li, Tao. "Laminar Branched Surfaces in 3-manifolds." Geometry and Topology 6.153 (2002): 194.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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