Related papers: Orbit categories, classifying spaces, and generali…
In this paper we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric…
A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…
A categorical generalization of the notion of movability from the inverse systems and shape theory was given by the first author who defined the notion of movable category and interpreted by this the movability of topological spaces. In…
We lift Charles Rezk's complete Segal space model structure on the category of simplicial spaces to a Quillen equivalent one on the category of relative categories.
A simple orbit classification constraint extension to stellar dynamical modeling using Schwarzschild's method is demonstrated. The classification scheme used is the existing `orbit circularity' scheme (lambda_z) where orbits are split into…
We give a general method that may be effectively applied to the question of whether two components of a function space have the same homotopy type. We describe certain group-like actions on function spaces. Our basic results assert that if…
Building on work by Fiore-Pronk-Paoli, we construct four model structures on the category of double categories, each modeling one of the following: simplicial spaces, Segal spaces, $(\infty,1)$-categories, and $\infty$-groupoids.…
We study orbit spaces of generalized gradient vector fields for Morse functions. Typically, these orbit spaces are non-Hausdorff. Nevertheless, they are quite structured topologically and are amenable to study. We show that these orbit…
We develop the basic theory of Maurer-Cartan simplicial sets associated to (shifted complete) $L_\infty$ algebras equipped with the action of a finite group. Our main result asserts that the inclusion of the fixed points of this equivariant…
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the…
We describe a simple algorithm for classifying orbits into orbit families. This algorithm works by finding patterns in the sign changes of the principal coordinates. Orbits in the logarithmic potential are studied as an application; we…
We compute the mapping class group orbits in the homotopy set of framings of a compact connected oriented surface with non-empty boundary. In the case $g > 1$ the computation is some modification of Johnson's results and certain arguments…
We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of…
Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…
In order to get $\lambda$-models with a rich structure of $\infty$-groupoid, which we call "homotopy $\lambda$-models", a general technique is described for solving domain equations on any cartesian closed $\infty$-category (c.c.i.) with…
We generalize the notion of a bornology by omitting the condition that a one-point-subset is bounded and obtain a complete and co-complete generalization of the category of bornological coarse spaces. Then we imitate the construction of…
We construct a category that classifies compact Hausdorff spaces by their shape and finite topological spaces by their weak homotopy type.
The category of monotone determined spaces is an extended topological framework for dcpos in domain theory. We first show that monotone determined spaces are exactly the spaces generated by one-point convergence spaces, and then naturally…
Given a suitable functor T:C -> D between model categories, we define a long exact sequence relating the homotopy groups of any X in C with those of TX, and use this to describe an obstruction theory for lifting an object G in D to C.…
Let $R\subseteq \Bbb Q$ be a subring of the rationals and let $p$ be the least prime (if none, $p=\infty $) which is not invertible in $R.$ For an $R$-local $r$-connected $CW$-complex $X$ of dimension $\leq \min(r+2p-3,rp-1), r\geq 1, $ a…