7
votes
1answer
181 views
Question about tetrahedron decomposition
Are there tetrahedra which can be subdivided into three parts similar to the original? I believe this would require splitting one face into three parts. I know some types of tetrah …
1
vote
1answer
99 views
Vector fields on a simplicial manifold.
Is there a known definition of vector fields on a simplicial manifold?
For me, it seems natural that the definition should be something along the lines: Let $M_{\bullet}$ be a si …
5
votes
1answer
214 views
Does every simplicial polytope have a topology-preserving contractible edge?
An edge of a triangulated manifold is said to be contractible if it may be contracted to a vertex without modifying the topological type of the underlying manifold. Otherwise, the …
2
votes
0answers
117 views
Explicit Lie May structure on cosimplicial DG Lie algebras
In the paper "Homotopy Lie algebras", Schechtman and Hinich proved that any cosimplicial
differential graded Lie algebra has the structure of a 'Lie May algebra'.
If my understan …
3
votes
0answers
95 views
Is there a local projective model structure on simplicial sheaves? What are its fibrant objects?
Consider a site S (I am mostly interested in hypercomplete sites, e.g., the site of smooth manifolds).
The category of simplicial presheaves SPSh(S) on S can be equipped with the l …
4
votes
2answers
297 views
Removing a simplicial subset from a simplicial set
Let $A, X$ be simplicial sets, and suppose there's an inclusion $A \longrightarrow X$. Geometrically realizing the inclusion map, we get a pair of spaces $(\mathcal{A}, \mathcal{X …
7
votes
2answers
279 views
Combinatorial distance between simplicial complexes
Let $K_1$ and $K_2$ be two simplicial complexes.
I am seeking a measure of the distance between $K_1$ and $K_2$ when
viewed as combinatorial objects.
What I have in mind is somethi …
16
votes
3answers
295 views
Testing simplicial complexes for shellability
Question
Are there efficient algorithms to check if a finite simplicial complex defined in terms of its maximal facets is shellable?
By efficient here I am willing to consid …
2
votes
1answer
193 views
Path components of a monoidal category acting on homology
Let $S$ be a (small) symmetric monoidal category and $X$ a (small) category on which $S$ acts. $\pi_0(S) = \pi_0(BS)$ is naturally an abelian monoid, with $[A] + [B] := [A+B]$, wh …
1
vote
1answer
126 views
How to call a simplicial set where every boundary of a simplex can be filled?
What is the correct terminology for the following property of a simplicial set $X_\bullet$:
For every $k\geq 0$, every map $\partial\Delta^k\to X_\bullet$ can be extended to a …
2
votes
0answers
93 views
Simplicial chain complex with ordered simplices
Let $X$ be an abstract simplicial complex. Recall that the usual simplicial chain complex for $X$ is defined as follows. Let $C_k(X)$ be the quotient of the free abelian group on …
1
vote
1answer
100 views
homology of $B S^{-1} S$ computation in the proof that $+ = Q$
Let $S$ denote the category of projective (left) $R$-modules with isomorphisms for arrows. We have that
$BS^{-1}S \sim B \text{GL}(R)^+ \times K_0(R)$
In proving this, in Sri …
12
votes
2answers
398 views
Multisimplicial geometric realization
Does anyone know a reference or proof for the following? Let $k\geq 1$ and let $X$ be a space. There is a $k$-fold multisimplicial set whose simplices in degree $n_1,\ldots,n_k$ …
7
votes
3answers
228 views
When is the projective model structure cartesian? When is the internal hom invariant?
If M is a sufficiently nice model category and D is a small category then there are two natural model structures we can impose on the functor category $Fun(D,M)$ where the weak equ …
2
votes
2answers
229 views
Simplicial path and loop spaces
I am trying to understand the relationship between the simplicial path space and loop space with the path space of a topological space, and the loop space of a topological space.
…

