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- ==Simplicial maps== ...to see map $h$ as a “realization”<!--\index{realization}--> $h=|f|$ of a “simplicial” map $f:K\to L$ between these complexes:34 KB (5,897 words) - 16:05, 26 October 2015
- ...to see map $h$ as a “realization”<!--\index{realization}--> $h=|f|$ of a “simplicial” map $f:K\to L$ between these complexes: ...s of a “collapse”<!--\index{collapse}-->. Since graphs are $1$-dimensional simplicial complexes, we can rewrite those definitions using the language of simplices34 KB (5,929 words) - 03:31, 29 November 2015
- ==Simplicial vs cell complexes== *''simplicial complexes''<!--\index{simplicial complex}-->: cells are homeomorphic to points, segments, triangles, tetrahedra, ...30 KB (5,172 words) - 21:52, 26 November 2015
- <!--s-->[[Image:example graph and simplicial complex.png|center]] This data set is called a ''simplicial complex''<!--\index{simplicial complex}--> (or sometimes even a “multi-graph”). Its elements are called $0$-,30 KB (5,021 words) - 13:42, 1 December 2015
- <!--s-->[[Image:example graph and simplicial complex.png|center]] This data set is called a ''simplicial complex''<!--\index{simplicial complex}--> (or sometimes even a “multi-graph”). Its elements are called $0$-,31 KB (5,219 words) - 15:07, 2 April 2016
- Previously, we proved that if complex $K^1$ is obtained from complex $K$ via a sequence of elementary collapses, then Suppose the circle is given by the simplest cell complex with just two cells $A,a$. Let's list ''all'' maps that can be represented51 KB (9,162 words) - 15:33, 1 December 2015
- ==Simplicial complexes== Recall that a chain complex<!--\index{chain complex}--> is a sequence of vector spaces and linear operators:31 KB (5,170 words) - 13:44, 1 December 2015
- [[image:cubical complex distorted.png|center]] [[image:cubical complex bent.png|center]]42 KB (7,131 words) - 17:31, 30 November 2015
- *[[abstract simplicial complex|abstract simplicial complex]] *[[augmented chain complex|augmented chain complex]]16 KB (1,773 words) - 00:41, 17 February 2016
- <!--75-->[[image:cubical complex distorted.png| center]] <!--75-->[[image:cubical complex bent.png| center]]35 KB (5,871 words) - 22:43, 7 April 2016
- ...recall the mechanical interpretation of a realization $|K|$ of a geometric complex $K$ of ambient dimension $n=1$: ...rods using an extra set of rods (and hinges) that form a new, Hodge-dual, complex $K^{\star}$.20 KB (3,354 words) - 17:37, 30 November 2015
- [[image:simplicial tangent spaces on graph.png|center]] '''Definition.''' For each vertex $A$ in a cell complex $K$, the (dimension $1$) ''tangent space'' at $A$ of $K$ is the set of $1$-49 KB (8,852 words) - 00:30, 29 May 2015
- '''Theorem (Fundamental Theorem of Algebra).''' Every non-constant (complex) polynomial has a root. ...is question seems too challenging indicates that the ''domain space is too complex''!46 KB (7,846 words) - 02:47, 30 November 2015
- Let's recall the mechanical interpretation of a realization $|K|$ of a metric complex $K$ of dimension $n=1$: ...rods using an extra set of rods (and hinges) that form a new, Hodge-dual, complex $K^{\star}$.21 KB (3,445 words) - 13:53, 19 February 2016
- '''Theorem (Fundamental Theorem of Algebra).''' Every non-constant (complex) polynomial has a root. ...is question seems too challenging indicates that the ''domain space is too complex''!45 KB (7,738 words) - 15:18, 24 October 2015
- Below, we will see how the theory of simplicial maps and their homology is extended to general cell complexes. We take the lead from simplicial maps. Under a simplicial map $f$, every $n$-cell $s$ is either42 KB (7,005 words) - 03:10, 30 November 2015
- [[File:Simplicial complex example.svg|thumb|200px|A simplicial 3-complex.]] A '''simplicial complex''' <math>\mathcal{K}</math> is a set of [[Simplex|simplices]] that satisfie27 KB (4,329 words) - 16:02, 1 September 2019
- Below, we will see how the theory of simplicial maps is extended to general cell complexes. We take the lead from simplicial maps: every $n$-cell $s$ is either cloned, $f(s) \approx s$, or collapsed,31 KB (5,330 words) - 22:14, 14 March 2016
- Below we will see how the theory of simplicial maps and their homology is extended to general cell complexes. We take the lead from simplicial maps. Under a simplicial map $f$, every $n$-cell $s$ is either41 KB (6,926 words) - 02:14, 21 October 2015
- ...s approach has been extensively applied to digital image analysis [11] and geometric modeling [15]. This method of cell decomposition differs in technical detai The cell decomposition also makes certain geometric concepts more straightforward. First, an object and its background share ed41 KB (6,854 words) - 15:05, 28 October 2011