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A Banach algebra A is called simplicially amenable if H"(A)=0 for all n > 0 (or,
equivalently, H,t(/1) = 0 for all n > 0, and H0(A) is Hausdorff). Combining
Theorems 2.4.19 (for X = A*) and 2.4.20, we immediately have PROPOSITION
2.6.2.
2
Categories in Algebra, Geometry and Mathematical Physics: ...
Given any crossed complex C, there is a simplicially enriched groupoid which
can be constructed from it, and such that the corresponding Moore complex is
isomorphic to C. This relationship between crossed complexes and 'simplicial ...
3
Model Categories and Their Localizations
In addition, simplicially homotopic maps of simplicial sets induce simplicially
homotopic maps in a simplicial model category (see Lemma 9.5.17). Definition
9.5.2. Let M be a simplicial model category, let X and Y be objects of M, and let g
and ...
Philip S. Hirschhorn,
2009
4
Categorical Homotopy Theory
If, however, we replace the Kan extension defining L by its enriched analog,
defined in (7.6.7), then this functor is simplicially enriched. Exercise 3.7.18 Let
Mbe cocomplete. Show that the categoryM op of simplicial objects in M is
simplicially ...
5
Topology II: Homotopy and Homology. Classical Manifolds
The complete subspaces of the space Si A (see E above) are precisely the
spaces Si B with B c A. H. A map of a simplicial space X to a simplicial space Y is
said to be simplicial if it maps each simplex of X simplicially to a simplex of Y.
Such a ...
S.P. Novikov, V.A. Rokhlin,
2004
6
Smoothings of Piecewise Linear Manifolds
Suppose then that d : |St(v)| -» Rm_1 x R is a PL embedding such that n^d = A.
Let C be a subdivision of C in which fl is simplicially affine. Given s > 0, let r>0 be
so small that if w ( |Stc(v)| - |dStc(v is a vertex of C and |y-A(w)| < r, there exists a ...
Morris W. Hirsch, Barry Mazur,
1974
7
Spaces of PL Manifolds and Categories of Simple Maps
We say that a finite non—singular simplicial set X is simplicially collapsible if for
some vertex v of X there is a simplicial expansion {v} C X, cf. Definition 3.2.1(d).
By [Wh39, Thms. 6 and 7], any triangulation of [Ag] admits a subdivision that is ...
Friedhelm Waldhausen, Bjørn Jahren, John Rognes,
2013
8
S-modules in the Category of Schemes
Each prespectrum is levelwise simplicially weak equivalent to a levelwise
simplicially fibrant prespectrum, which can be made functorial. We recall a
description of this fibrant replacement functor. By the simplicial model structure
on Spc(S),, ...
9
Efficient Graph Representations.: The Fields Institute for ...
In general, fc-simplicially reducible graphs are not equivalent to graphs without
holes of size > k (exercise 12.7). Chordal bipartite graphs are equivalent to
bipartite graphs with 5-simplicial elimination schemes (exercise 9.3) It is not clear
...
10
Two-Dimensional Homotopy and Combinatorial Group Theory
However, by Zeeman ([Ze63-66], Chapters I and III), it follows that, for any
triangulation of a topological n-ball, there is an integer k such that the k-th
barycentric subdivision of the triangulation is simplicially collapsible. A result of
Chillingworth ...
Cynthia Hog-Angeloni, Wolfgang Metzler, Allan J. Sieradski,
1993