摘要 :
In previous work we defined a Quillen model structure, determined by cycles,on the category Gph of directed graphs. In this paper we give a complete description of the homotopy category of graphs associated to our model structure....
展开
In previous work we defined a Quillen model structure, determined by cycles,on the category Gph of directed graphs. In this paper we give a complete description of the homotopy category of graphs associated to our model structure. We endow the categories of N-sets and Z-sets with related modelstructures, and show that their homotopy categories are Quillen equivalent tothe homotopy category Ho(Gph). This enables us to show that Ho(Gph) isequivalent to the category cZSet of periodic Z-sets, and to show that two finitedirected graphs are almost-isospectral if and only if they arehomotopy-equivalent in our sense.
收起
摘要 :
Steenrod operations were defined by Voedvodsky in motivic cohomology in order to prove the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings. The purpose of this paper is to p...
展开
Steenrod operations were defined by Voedvodsky in motivic cohomology in order to prove the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings. The purpose of this paper is to provide a setting for the construction of the Steenrod operations in algebraic geometry, for generalized cohomology theories whose formal group law has order two. We adapt the methods used by Bisson-Joyal in studying Steenrod and Dyer-Lashof operations in unoriented cobordism and mod 2 cohomology.
收起
摘要 :
The purpose of this paper is to develop a homotopical algebra for graphs, relevant to the zeta series and the spectra of finite graphs. More precisely, we define a Quillen model structure in a category of graphs (directed and poss...
展开
The purpose of this paper is to develop a homotopical algebra for graphs, relevant to the zeta series and the spectra of finite graphs. More precisely, we define a Quillen model structure in a category of graphs (directed and possibly infinite, with loops and multiple arcs allowed). The weak equivalences for this model structure are the Acyclics (graph morphisms which preserve cycles). The cofibrations and fibrations for the model are determined from the class of Whiskerings (graph morphisms produced by grafting trees). Our model structure seems to fit well with the importance of acyclic directed graphs in many applications.
收起
摘要 :
We show that a compact affine manifold endowed with an affine Anosov transformation is finitelycovered by a complete affine nilmanifold. This is a partial answer of a conjecture of Franks foraffine manifolds.
原文获取