|
In the mathematical discipline of simplicial homology theory, a simplicial map is a map between simplicial complexes with the property that the images of the vertices of a simplex always span a simplex. Note that this implies that vertices have vertices for images. Simplicial maps are thus determined by their effects on vertices. In particular, there are a finite number of simplicial maps between two given finite simplicial complexes. Simplicial maps induce continuous maps between the underlying polyhedra of the simplicial complexes: one simply extends linearly using barycentric coordinates. Simplicial maps which are bijective are called ''simplicial isomorphisms''. ==Simplicial approximation== Let be a continuous map between the underlying polyhedra of simplicial complexes and let us write for the star of a vertex. A simplicial map such that , is called a simplicial approximation to . A simplicial approximation is homotopic to the map it approximates. 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「simplicial map」の詳細全文を読む スポンサード リンク
|