An **incompressible surface** is a concept from the field of topology, specifically in the study of 3-manifolds. It refers to a two-dimensional surface that cannot be compressed into a simpler form without cutting it. This property is significant in both mathematical theory and applications, such as in knot theory and the study of 3-manifolds.
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An incompressible surface is a properly embedded two-sided topological surface with no compressing disk, subject to the usual exclusion of inessential spherical components. A compressing disk has boundary an essential closed curve on the topological surface and interior disjoint from it.