Related papers: Representations up to coherent homotopy
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a…
We prove that strongly homotopy algebras (such as $A_\infty$, $C_\infty$, sh Lie, $B_\infty$, $G_\infty$,...) are homotopically invariant in the category of chain complexes. An important consequence is a rigorous proof that `strongly…
Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…
The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy…
The study of homotopy theoretic phenomena in the language of type theory is sometimes loosely called `synthetic homotopy theory'. Homotopy theory in type theory is only one of the many aspects of homotopy type theory, which also includes…
In "On the homotopy theory of arrangements," published in 1986, the authors gave a comprehensive survey of the subject. This article updates and continues the earlier article, noting some key open problems.
We investigate to what extent persistent homology benefits from the properties of the usual homology theory.
We propose a new approach to crystalline cohomology based on the observation that one can lift smooth algebras uniquely "up to coherent homotopy."
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
Correspondence homomorphisms are both a generalization of standard homomorphisms and a generalization of correspondence colourings. For a fixed target graph $H$, the problem is to decide whether an input graph $G$, with each edge labeled by…
We observe that the notion of two sets being equal up to finitely many elements is a homotopy equivalence relation in a model category, and suggest a homotopy-invariant variant of Generalised Continuum Hypothesis about which more can be…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
Coherent states for equally spaced, homogeneous waveguide arrays are defined, in the infinite, semiinfinite and finite cases, and resolutions of the identity are constructed, using different methods. In the infinite case, which corresponds…
Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.
The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The area has seen several fundamentally important results that are…
Covering numbers of convex bodies based on homothetical copies and related illumination numbers are well-known in combinatorial geometry and, for example, related to Hadwiger's famous covering problem. Similar numbers can be defined by…
Given based cellular spaces X and Y, X compact, we define a sequence of increasingly fine equivalences on the based-homotopy set [X,Y].
We construct a system of coherent states for the hydrogen atom that is expressed in terms of elementary functions. Unlike to the previous attempts in this direction, this system possesses the properties equivalent to the most of those for…
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…