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Results tagged with simplicial-complexes
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user 115363
4
votes
1
answer
181
views
What is a sufficient set of links in a simplicial complex to represent any PL manifold?
The link of a vertex in a $n$-dimensional simplicial complex is the $(n-1)$-dimensional simplicial complex formed by the $(n-1)$-simplices each of which, together with the vertex, spans an $n$-simplex …
- 2,839
2
votes
Accepted
Are there invariants of cell complexes similar to the Euler characteristic?
As pointed out in the comments, every characteristic class in $H^d(BO(d), G)$ provides a $G$-valued locally computable invariant of $d$-manifolds, by pulling back via the classifying map of the tangen …
- 2,839
2
votes
Are there invariants of cell complexes similar to the Euler characteristic?
Meanwhile it seems to me that the discrete analogues to all Stiefel-Whitney numbers of $d$-dimensional manifolds are invariants of this type:
First, for every $n$ there is a rule to color every $d-n$ …
- 2,839
9
votes
3
answers
368
views
Are there invariants of cell complexes similar to the Euler characteristic?
The Euler characteristic is an invariant (under homeomorphism) of manifolds that can be computed from a cellulation by (weighted) counting of different kinds of objects, namely
\begin{equation}
\chi=\ …
- 2,839
12
votes
3
answers
561
views
Is there a discrete lattice analogue of conformal transformations?
There is a simple discrete combinatorial analogue of manifolds and homeomorphisms: Replace manifolds by simplicial complexes and homeomorphisms by Pachner moves. Equivalence classes of manifolds under …
- 2,839
8
votes
0
answers
158
views
Is there a combinatorial representation of general topological manifolds similar to triangul...
Piece-wise linear manifolds are combinatorially represented by simplicial complexes modulo Pachner moves. However, for dimensions greater than $3$, the notions of piece-wise linear and topological man …
- 2,839
3
votes
0
answers
118
views
Which Stiefel-Whitney numbers can be extended to manifolds with boundaries?
The Stiefel-Whitney numbers are classical topological manifold invariants obtained by integrating some local quantity (a cup product of Stiefel-Whitney classes) over the manifold. Which Stiefel-Whitne …
- 2,839