翻訳と辞書 Words near each other ・ Quasisimnia ・ Quasisimnia hirasei ・ Quasisimnia robertsoni ・ Quasisimple group ・ Quasispecies model ・ Quasistatic ・ Quasistatic approximation ・ Quasistatic loading ・ Quasistatic process ・ Quasisymmetric ・ Quasisymmetric function ・ Quasisymmetric map ・ Quasit ・ Quasithin group ・ Quasitopological space ・ Quasitoric manifold ・ Quasitransitive relation ・ Quasitriangular Hopf algebra ・ Quasiturbine ・ Quasivariety ・ Quasquara ・ Quasqueton, Iowa ・ Quassaick Creek ・ Quassar ・ Quassel IRC ・ Quassia ・ Quassia amara ・ Quassia sanguinea ・ Quassia sp. 'Moonee Creek' ・ Quassia sp. 'Mount Nardi' 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 Quasitoric manifold ： ウィキペディア英語版 Quasitoric manifold In mathematics, a quasitoric manifold is a topological analogue of the nonsingular projective toric variety of algebraic geometry. A smooth $2n$-dimensional manifold is a quasitoric manifold if it admits a smooth, locally standard action of an $n$-dimensional torus, with orbit space an $n$-dimensional simple convex polytope. Quasitoric manifolds were introduced in 1991 by M. Davis and T. Januszkiewicz,〔M. Davis and T. Januskiewicz, 1991.〕 who called them "toric manifolds". However, the term "quasitoric manifold" was eventually adopted to avoid confusion with the class of compact smooth toric varieties, which are known to algebraic geometers as toric manifolds.〔V. Buchstaber and T. Panov, 2002.〕 Quasitoric manifolds are studied in a variety of contexts in algebraic topology, such as complex cobordism theory, and the other oriented cohomology theories.〔V. Buchstaber and N. Ray, 2008.〕 ==Definitions== Denote the $i$-th subcircle of the $n$-torus $T^n$ by $T\_i$ so that $T\_1\; \backslash times\; \backslash ldots\; \backslash times\; T\_n\; =\; T^n$. Then coordinate-wise multiplication of $T^n$ on $\backslash mathbb^n$ is called the standard representation. Given open sets $X$ in $M^$ and $Y$ in $\backslash mathbb^n$, that are closed under the action of $T^n$, a $T^$-action on $M^$ is defined to be locally isomorphic to the standard representation if $h(tx)\; =\; \backslash alpha(t)h(x)$, for all $t$ in $T^n$, $x$ in $X$, where $h$ is a homeomorphism $X\; \backslash rightarrow\; Y$, and $\backslash alpha$ is an automorphism of $T^n$. Given a simple convex polytope $P^n$ with $m$ facets, a $T^n$-manifold $M^$ is a quasitoric manifold over $P^n$ if, # the $T^n$-action is locally isomorphic to the standard representation, # there is a projection $\backslash pi\; :\; M^\; \backslash rightarrow\; P^n$ that maps each $l$-dimensional orbit to a point in the interior of an $l$-dimensional face of $P^n$, for $l\; =\; 0,$ $...,$ $n$. The definition implies that the fixed points of $M^$ under the $T^n$-action are mapped to the vertices of $P^n$ by $\backslash pi$, while points where the action is free project to the interior of the polytope. 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「Quasitoric manifold」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.