Barycentric subdivision
of a geometric complex
A complex obtained by replacing the simplices of
by smaller ones by means of the following procedure. Each one-dimensional simplex (segment) is halved. On the assumption that all simplices of dimension
are already subdivided, the subdivision of any
-dimensional simplex
is defined by means of cones over the simplices of the boundary of
with a common vertex that is the barycentre of the simplex
, i.e. the point with barycentric coordinates
. The vertices of the resulting complex
are in a one-to-one correspondence with the simplices of the complex
, while the simplices of the complex
are in such a correspondence with inclusion-ordered finite tuples of simplices from
. The formal definition of a barycentric subdivision for the case of an abstract complex is analogous.
Comments
References
[a1] | K. Lamotke, "Semisimpliziale algebraische Topologie" , Springer (1968) |
Barycentric subdivision. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Barycentric_subdivision&oldid=14992