Related papers: The homotopy branching space of a flow
Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium in response to the flow, in turn causing flow pathways to evolve. We…
We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem of Moore concerning the homology of…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the…
Let $M$ be a differentiable manifold endowed locally with two complementary distributions, say horizontal and vertical. We consider the two subgroups of (local) diffeomorphisms of $M$ generated by vector fields in each of of these…
The question of whether a given H-space X is, up to homotopy, a loop space has been studied from a variety of viewpoints. Here we address this question from the aspect of homotopy operations, in the classical sense of operations on homotopy…
Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
Modular flow is a symmetry of the algebra of observables associated to spacetime regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is…
We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…
The purpose of this paper is to explain why the functor that sends a stratified topological space $S$ to the $\infty$-category of constructible (hyper)sheaves on $S$ with coefficients in a large class of presentable $\infty$categories is…
We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra…
Fix a prime $p$. Since their definition in the context of Localization Theory, the homotopy functors $P_{B\Z/p}$ and $CW_{B\Z/p}$ have shown to be powerful tools to understand and describe the mod $p$ structure of a space. In this paper, we…
Homotopy coherence has a considerable history, albeit also by other names. For this volume highlighting symmetries, the appropriate use is: Homotopy coherence of representations, at one time known as strong homotopy representations. We…
We reconsider formulating $D$ dimensional gauge theories, with the focus on the case of gravity theories, in spacetimes with boundaries. We extend covariant phase space formalism to the cases in which boundaries are allowed to fluctuate. We…
This mostly expository paper records some basic facts about towers of homotopy fiber sequences. We give a proof that a pairing of towers induces a pairing of associated spectral sequences, for towers of spaces and towers of spectra.
This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…
Discrete homotopy theory or A-homotopy theory is a combinatorial homotopy theory defined on graphs, simplicial complexes, and metric spaces, reflecting information about their connectivity. The present paper aims to further understand the…
It is a generally shared opinion that significant information about the topology of a bounded domain $\Omega $ of a riemannian manifold $M$ is encoded into the properties of the distance, $d_{\partial\Omega}$, %, $d:\Omega\rightarrow…
This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group.…