翻訳と辞書 Words near each other ・ Bounty Bowl ・ Bounty Day ・ Bounty Fresh Chicken ・ Bounty Hamster ・ Bounty Hounds ・ Bounty hunter ・ Bounty hunter (disambiguation) ・ Bounty Hunter Bloods ・ Bounty Hunters (TV series) ・ Boundary Waters Treaty of 1909 ・ Boundary Waters–Canadian derecho ・ Boundary, Derbyshire ・ Boundary, Leicestershire ・ Boundary, Staffordshire ・ Boundary, Washington ・ Boundary-incompressible surface ・ Boundary-Layer Meteorology ・ Boundary-Similkameen ・ Boundary-value analysis ・ Boundary-Waneta Border Crossing ・ Boundary-work ・ Boundaryless organization ・ Bounded Choice ・ Bounded complete poset ・ Bounded deformation ・ Bounded emotionality ・ Bounded expansion ・ Bounded function ・ Bounded growth ・ Bounded inverse theorem Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Boundary-incompressible surface ： ウィキペディア英語版 Boundary-incompressible surface In low-dimensional topology, a boundary-incompressible surface is a two-dimensional surface within a three-dimensional manifold whose topology cannot be made simpler by a certain type of operation known as boundary compression. Suppose ''M'' is a 3-manifold with boundary. Suppose also that ''S'' is a compact surface with boundary that is properly embedded in ''M'', meaning that the boundary of ''S'' is a subset of the boundary of ''M'' and the interior points of ''S'' are a subset of the interior points of ''M''. A boundary-compressing disk for ''S'' in ''M'' is defined to be a disk ''D'' in ''M'' such that $D\; \backslash cap\; S\; =\; \backslash alpha$ and $D\; \backslash cap\; \backslash partial\; M\; =\; \backslash beta$ are arcs in $\backslash partial\; D$, with $\backslash alpha\; \backslash cup\; \backslash beta\; =\; \backslash partial\; D$, $\backslash alpha\; \backslash cap\; \backslash beta\; =\; \backslash partial\; \backslash alpha\; =\; \backslash partial\; \backslash beta$, and $\backslash alpha$ is an essential arc in ''S'' ($\backslash alpha$ does not cobound a disk in ''S'' with another arc in $\backslash partial\; S$). The surface ''S'' is said to be boundary-compressible if either ''S'' is a disk that cobounds a ball with a disk in $\backslash partial\; M$ or there exists a boundary-compressing disk for ''S'' in ''M''. Otherwise, ''S'' is boundary-incompressible. Alternatively, one can relax this definition by dropping the requirement that the surface be properly embedded. Suppose now that ''S'' is a compact surface (with boundary) embedded in the boundary of a 3-manifold ''M''. Suppose further that ''D'' is a properly embedded disk in ''M'' such that ''D'' intersects ''S'' in an essential arc (one that does not cobound a disk in ''S'' with another arc in $\backslash partial\; S$). Then ''D'' is called a boundary-compressing disk for ''S'' in ''M''. As above, ''S'' is said to be boundary-compressible if either ''S'' is a disk in $\backslash partial\; M$ or there exists a boundary-compressing disk for ''S'' in ''M''. Otherwise, ''S'' is boundary-incompressible. For instance, if ''K'' is a trefoil knot embedded in the boundary of a solid torus ''V'' and ''S'' is the closure of a small annular neighborhood of ''K'' in $\backslash partial\; V$, then ''S'' is not properly embedded in ''V'' since the interior of ''S'' is not contained in the interior of ''V''. However, ''S'' is embedded in $\backslash partial\; V$ and there does not exist a boundary-compressing disk for ''S'' in ''V'', so ''S'' is boundary-incompressible by the second definition. == See also == * Incompressible surface 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Boundary-incompressible surface」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.