theory of simplicial sets, a simplicial group is a simplicial object in the category of groups. Similarly, a simplicial abelian group is a simplicial object...
2 KB (246 words) - 19:12, 4 August 2024
simplicial set appearing in modern simplicial homotopy theory. The purely combinatorial counterpart to a simplicial complex is an abstract simplicial...
11 KB (1,724 words) - 12:40, 5 June 2024
In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of...
17 KB (2,171 words) - 08:50, 19 June 2024
In mathematics, a simplicial set is an object composed of simplices in a specific way. Simplicial sets are higher-dimensional generalizations of directed...
23 KB (3,327 words) - 19:12, 4 March 2024
In combinatorics, an abstract simplicial complex (ASC), often called an abstract complex or just a complex, is a family of sets that is closed under taking...
17 KB (2,486 words) - 07:30, 29 May 2024
to a simplicial complex, its fundamental group can be described explicitly in terms of generators and relations. If X is a connected simplicial complex...
53 KB (8,076 words) - 07:10, 6 August 2024
Kan fibration (category Simplicial sets)
part of the theory of simplicial sets. Kan fibrations are the fibrations of the standard model category structure on simplicial sets and are therefore...
15 KB (2,791 words) - 17:29, 16 April 2024
functor from the site to the category of simplicial sets). Equivalently, a simplicial presheaf is a simplicial object in the category of presheaves on...
6 KB (821 words) - 08:05, 7 March 2024
Homology (mathematics) (redirect from Homology group)
The simplicial homology groups Hn(X) of a simplicial complex X are defined using the simplicial chain complex C(X), with Cn(X) the free abelian group generated...
54 KB (8,218 words) - 14:50, 22 August 2024
1)} through a simplicial construction, and it behaves functorially. This construction gives an equivalence between groups and 1-groups. Note that some...
13 KB (2,037 words) - 23:36, 26 April 2024
In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by...
4 KB (636 words) - 16:53, 13 May 2024
Orbifold (redirect from Orbifold fundamental group)
its edge-path group is isomorphic to that of Z. If a countable discrete group acts by a regular simplicial proper action on a simplicial complex, the quotient...
78 KB (10,240 words) - 18:02, 26 July 2024
The simplicial complex recognition problem is a computational problem in algebraic topology. Given a simplicial complex, the problem is to decide whether...
4 KB (501 words) - 16:59, 29 January 2024
Algebraic topology (section Homotopy groups)
work with. The fundamental group of a (finite) simplicial complex does have a finite presentation. Homology and cohomology groups, on the other hand, are...
19 KB (2,081 words) - 18:42, 13 April 2024
Dold–Kan correspondence (category Simplicial sets)
complexes and the category of simplicial abelian groups. Moreover, under the equivalence, the n {\displaystyle n} th homology group of a chain complex is the...
5 KB (808 words) - 14:17, 27 August 2024
Triangulation (topology) (section Simplicial complexes)
the choice of a homeomorphism in a suitable simplicial complex. Spaces being homeomorphic to a simplicial complex are called triangulable. Triangulation...
33 KB (5,220 words) - 12:29, 17 May 2024
In physics, the term simplicial manifold commonly refers to one of several loosely defined objects, commonly appearing in the study of Regge calculus....
2 KB (216 words) - 23:19, 12 May 2024
correspondence: simplicial abelian groups correspond to chain complexes of abelian groups, so a higher stack modeled as a simplicial group should correspond...
7 KB (892 words) - 11:05, 18 February 2024
Real tree (redirect from Simplicial R-tree)
metric spaces generalising simplicial trees. They arise naturally in many mathematical contexts, in particular geometric group theory and probability theory...
11 KB (1,593 words) - 08:17, 27 June 2024
algebra, a simplicial commutative ring is a commutative monoid in the category of simplicial abelian groups, or, equivalently, a simplicial object in the...
3 KB (519 words) - 17:58, 31 July 2024
about groups by studying group actions on simplicial trees. External precursors of geometric group theory include the study of lattices in Lie groups, especially...
38 KB (4,308 words) - 13:31, 7 April 2024
Delta set (redirect from Semi-simplicial set)
In mathematics, a Δ-set, often called a Δ-complex or a semi-simplicial set, is a combinatorial object that is useful in the construction and triangulation...
14 KB (2,624 words) - 21:40, 9 April 2024
algebraic geometry. It is used in calculating the homotopy properties of a simplicial group. Srinivas, Vasudevan (2013). Algebraic K-Theory. Springer Science &...
2 KB (182 words) - 05:32, 13 May 2024
Discrete geometry (section Simplicial complexes)
illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory...
15 KB (1,576 words) - 19:04, 13 July 2024
Bass–Serre theory (category Group theory)
of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions...
41 KB (5,901 words) - 05:59, 12 January 2024
Barycentric subdivision (category Simplicial homology)
is an operation on simplicial complexes. In algebraic topology it is sometimes useful to replace the original spaces with simplicial complexes via triangulations:...
16 KB (2,530 words) - 15:21, 13 June 2024
sequence. Quillen spectral sequence for calculating the homotopy of a simplicial group. Rothenberg–Steenrod spectral sequence is another name for the bar...
50 KB (10,702 words) - 12:49, 20 June 2024
of n-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW...
16 KB (2,508 words) - 10:59, 28 January 2024
calculus Simplex Simplicial manifold Spin foam Wayback Machine see Sec 6.8 Dynamics: III. Group field theory Freidel, L. (2005). "Group Field Theory: An...
4 KB (440 words) - 14:40, 20 May 2024
In geometry, the simplicial honeycomb (or n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the A ~ n {\displaystyle {\tilde...
10 KB (527 words) - 03:30, 24 July 2024