A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Khovanov spectra are shown to be functorial under certain conditions.
Clarifies sign ambiguity in Khovanov homology functoriality.
Extends Khovanov bracket to link cobordisms, proving functoriality up to scalars.
Simplifies fixing Khovanov homology functoriality.
Functorial properties of knot invariants under specific concordances.
Proves Khovanov homology functoriality and positivity for gl2 webs.
Clarifies properties of Ozsvath-Szabo contact invariant.
Unified framework for proving functoriality of various link homology theories.
Lie algebroids are by no means natural as an infinitesimal counterpart of groupoids. In this paper we propose a functorial construction called Nishimura algebroids for an infinitesimal counterpart of groupoids. Nishimura algebroids, intended for differential geometry, are of the same vein as Lawvere's functorial notion…
Study proves naturality and functoriality in a type of Heegaard Floer homology.
Anomaly in free fermion theory revealed in functorial field theory.
We prove that Morrison and Nieh's categorification of the su(3) quantum knot invariant is functorial with respect to tangle cobordisms. This is in contrast to the categorified su(2) theory, which was not functorial as originally defined. We use methods of Bar-Natan to construct explicit chain maps for each variation of…
Functorial semi-norms on singular homology give refined "size" information on singular homology classes. A fundamental example is the l^1-semi-norm. We show that there exist finite functorial semi-norms on singular homology that are exotic in the sense that they are not carried by the l^1-semi-norm.
Extends odd Khovanov bracket to link cobordisms and proves functoriality up to sign.
We prove that the bigraded colored Khovanov-Rozansky type A link and tangle invariants are functorial with respect to link and tangle cobordisms.
Functorial compactification of vector spaces defined as manifolds with corners.
In this paper, we prove a functorial aspect of the formal geometric quantization procedure of non-compact spin-c manifolds.
A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing maps in homology. Functorial semi-norms can be used to give constraints on the possible mapping degrees of maps between oriented manifolds. …
Quantum field theory uses Lorentzian bordisms to describe time evolution.
Alternative proof of Khovanov's up-to-sign functoriality for odd Khovanov homology.
Study normal bundle and deformation to get new pushforward maps.
In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology theory. As a preliminary we investigate functoriality in Morse homology. Functor…
We verify that the formula of X. Ma for the analytic torsion form of an iterated fibration implies that Lott's secondary analytic index is functorial.
The paper describes new types of picture-valued invariants and their applications.
Establishes functoriality of Baum-Bott residues under specific conditions.
This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and Mémoli to par…
The paper defines a category of Lagrangian correspondences in super Hilbert spaces and constructs a functorial field theory.
In this paper, we define the equivariant eta form of Bismut-Cheeger for a compact Lie group and establish a formula about the functoriality of equivariant eta forms with respect to the composition of two submersions.
Using the diagrammatic calculus for Soergel bimodules developed by B. Elias and M. Khovanov, we show that Rouquier complexes are functorial over braid cobordisms. We explicitly describe the chain maps which correspond to movie move generators.
Functoriality proved for higher rho invariants of elliptic operators.
We disprove the conjecture of M. Khovanov (math.QA/9908171) on the functoriality of his link homology with polynomial coefficients. This is in contrast to the case of integer coefficients, where functoriality was proved in math.GT/0206303 .
Functorial correspondence found between logarithmic connections and abelian connections.
Paper establishes equivalence between algebraic and functorial QFTs.
The Rips complex at scale r is homotopy equivalent to the nerve of a cover of diameter r.
To a Lie groupoid over a compact base, the associated group of bisection is an (infinite-dimensional) Lie group. Moreover, under certain circumstances one can reconstruct the Lie groupoid from its Lie group of bisections. In the present article we consider functorial aspects of these construction principles. The first …
Functorial maps and weak parities are equivalent descriptions of rules of substitution virtual crossings for classical in diagrams of a knot in a way compatible with Reidemeister moves. We introduce the notion of maximal weak parity and describe it for knots in a given closed oriented surface. This weak parity defines …
Refines a tangle invariant using XC-algebras.
We discuss two kinds of functorial prolongations of the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. We study the prolongation of vector fields in both cases and we prove that the bracket is preserved. Our proof is based on several new res…
Khovanov homology invariant proved for links in .
Spark complexes defined on good effective orbifold atlases.
We construct various functorial maps (projections) from virtual knots to classical knots. These maps are defined on diagrams of virtual knots; in terms of Gauss diagram each of them can be represented as a deletion of some chords. The construction relies upon the notion of parity. As corollaries, we prove that the mini…
Extends Khovanov homology to surfaces with singularities.
New obstructions found for Lagrangian cobordisms in knot Floer homology.
Constructs differential forms on -ringed spaces.
A homological invariant of 3-manifolds is defined, using abelian Yang-Mills gauge theory. It is shown that the construction, in an appropriate sense, is functorial with respect to the families of 4-dimensional cobordisms. This construction and its functoriality are used to define several link invariants. The strongest …
New modules derived from Khovanov homology for links.
New knot invariant from equivariant Heegaard Floer cohomology.
Investigates properties of moment maps and stratifications on Lie groups.