Related papers: Recognition principle for generalized Eilenberg-Ma…
This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…
Given based cellular spaces X and Y, X compact, we define a sequence of increasingly fine equivalences on the based-homotopy set [X,Y].
This paper presents a classification of the total spaces of $S^3$-bundles over $\mathbb{C}P^2$ up to orientation-preserving homotopy equivalence. Our approach proceeds in two steps: we first derive the PL-homeomorphism classification for…
We recall the complex structure on the generalised loop spaces $W^{k,2}(S,X)$, where $S$ is a compact real manifold with boundary and $X$ is a complex manifold, and prove a Hartogs-type extension theorem for holomorphic maps from certain…
The representation sets of central loops are investigated and the results obtained are used to construct a finite C-loop. It is shown that for certain types of isotopisms, the central identities are isotopic invariant.
We prove that many spaces of positive scalar curvature metrics have the homotopy type of infinite loop spaces. Our result in particular applies to the path component of the round metric inside $\mathcal{R}^+ (S^d)$ if $d \geq 6$. To achieve…
The aim of this note is to provide a comprehensive treatment of the homotopy theory of $\Gamma$-$G$-spaces for $G$ a finite group. We introduce two level and stable model structures on $\Gamma$-$G$-spaces and exhibit Quillen adjunctions to…
We show that the homotopy category of commutative algebra spectra over the Eilenberg-Mac Lane spectrum of the integers is equivalent to the homotopy category of E-infinity-monoids in unbounded chain complexes. We do this by establishing a…
We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages…
We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a $C^2$ differentiable map from a Hilbert space to a finite-dimensional…
This study first provides a brief overview of the structure of typical Grassmann manifolds. Then a new type of supergrassmannians is construced using an odd involution in a super ringed space and by gluing superdomains together. Next,…
We review our recent formulation of Colombeau type algebras as Hausdorff sequence spaces with ultranorms, defined by sequences of exponential weights. We extend previous results and give new perspectives related to echelon type spaces,…
We introduce a coarse analog of the classical Lusternik-Schnirelmann category which we denote by $\text{c-cat}$, defined for metric spaces in the coarse homotopy category. This provides a new tool for studying large-scale topological…
In a previous article, we introduced notions of finiteness obstruction, Euler characteristic, and L^2-Euler characteristic for wide classes of categories. In this sequel, we prove the compatibility of those notions with homotopy colimits of…
In this paper, we investigate equigeodesics on a compact homogeneous space $M=G/H.$ We introduce a formula for the identification of equigeodesic vectors only relying on the isotropy representation of $M$ and the Lie structure of the Lie…
We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized…
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…
In this note we characterize the distinguished boundary of the symmetrized polydisc and thereby develop a model theory for $\Gamma_n$-isometries along the lines of \cite{AY}. We further prove that for invariant subspaces of…
We introduce three generalizations of homotopy equivalence in digital images, to allow us to express whether a finite and an infinite digital image are similar with respect to homotopy. We show that these three generalizations are not…
In this paper we describe explicit $L_\infty$ algebras modeling the rational homotopy type of any component of the spaces $\map(X,Y)$ and $\map^*(X,Y)$ of free and pointed maps between the finite nilpotent CW-complex $X$ and the finite type…