Related papers: Rational Homotopy Equivalence

In many scientific and technological contexts we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal…

This paper defines homology in homotopy type theory, in the process stable homotopy groups are also defined. Previous research in synthetic homotopy theory is relied on, in particular the definition of cohomology. This work lays the…

The homology groups of a simplicial complex reveal fundamental properties of the topology of the data or the system and the notion of topological stability naturally poses an important yet not fully investigated question. In the current…

We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.

We provide a simple condition on rational cohomology for the total space of a pullback fibration over a connected sum to have the rational homotopy type of a connected sum, after looping. This takes inspiration from recent work of Jeffrey…

Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose…

We prove that the morphisms from a minimal Sullivan algebra $\Lambda V$ to $A_{PL}(|\Lambda V|)$, the algebra of polynomial differential forms on its realization, can be quasi-isomorphic if and only if the cohomology $H(\Lambda V)$ is of…

We investigate one-point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h-regular…

This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable to extract topological information from digital pictures. A simplicial complex is encoded in a (non-unique)…

We develop a homotopy theory of $L_\infty$ algebras based on the Lawrence-Sullivan construction, a complete differential graded Lie algebra which, as we show, satisfies the necessary properties to become the right cylinder in this category.…

We study surface representatives of homology classes of finite complexes which minimize certain complexity measures, including its genus and Euler characteristic. Our main result is that up to surgery at nullhomotopic curves minimizers are…

We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic…

We consider simplicial complexes that are generated from the binomial random 3-uniform hypergraph by taking the downward-closure. We determine when this simplicial complex is homologically connected, meaning that its zero-th and first…

We show that that classical rational homotopy theory in the sense of Sullivan [6] can be extended compactly supported setting. This presents a simplicial version of the compactly supported de Rham complex in characteristic zero, and proving…

We prove that the classifying space of a simplicial group is modeled by its homotopy coherent nerve.

In "On o-minimal homotopy groups", o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally…

Let p be a fibration of simply connected CW complexes with finite base B and fibre F. Let aut_1(p) denote the identity component of the space of all fibre-homotopy self-equivalences of p and Baut_1(p) the classifying space for this…

We extend classical tools from rational homotopy theory to topological data analysis by introducing persistent Sullivan minimal models of persistent topological spaces. Our main result establishes that the interleaving distance between such…

We build model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences determined by families of subgroups. In particular, by specifying to the family of graph subgroups (or, more…

A flag complex can be defined as a simplicial complex whose simplices correspond to complete subgraphs of its 1-skeleton taken as a graph. In this article, by introducing the notion of s-dismantlability, we shall define the s-homotopy type…