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.
Two graph homologies help compute embedding space.
Magnitude homology reveals that graphs can have torsion subgroups.
We study the hairy graph homology of a cyclic operad; in particular we show how to assemble corresponding hairy graph cohomology classes to form cocycles for ordinary graph homology, as defined by Kontsevich. We identify the part of hairy graph homology coming from graphs with cyclic fundamental group as the dihedral h…
Grid homology theory for spatial graphs extends skein sequence.
Grid homology properties for MOY graphs studied.
Extends Heisenberg homology to ribbon graphs.
Extends knot concordance invariant to balanced spatial graphs using grid homology.
The paper studies grid homology for spatial graphs and proves a Künneth formula for connected sums.
New homology theory connects graph domination to subtle algebraic structures.
Study on planar graph braid groups' second homology.
The paper reveals a property of chromatic homology for complete graphs.
The paper extends a knot invariant to graphs and connects it to homology cylinders.
Persistent homology enhances graph classification by capturing long-range graph properties.
J. Przytycki has established a connection between the Hochschild homology of an algebra and the chromatic graph homology of a polygon graph with coefficients in . In general the chromatic graph homology is not defined in the case where the coefficient ring is a non-commutative algebra. In this paper we define a …
Motivated by Khovanov homology and relations between the Jones polynomial and graph polynomials, we construct a homology theory for embedded graphs from which the chromatic polynomial can be recovered as the Euler characteristic. For plane graphs, we show that our chromatic homology can be recovered from the Khovanov h…
We introduce Khovanov homology for ribbon graphs and show that the Khovanov homology of a certain ribbon graph embedded on the Turaev surface of a link is isomorphic to the Khovanov homology of the link (after a grading shift). We also present a spanning quasi-tree model for the Khovanov homology of a ribbon graph.
In this thesis we work with Khovanov homology of links and its generalizations, as well as with the homology of graphs. Khovanov homology of links consists of graded chain complexes which are link invariants, up to chain homotopy, with graded Euler characteristic equal to the Jones polynomial of the link. Hence, it can…
Circle graph complexes reveal link properties via Khovanov homology.
Khovanov homology of a link and chromatic graph homology are known to be isomorphic in a range of homological gradings that depend on the girth of a graph. We discuss patterns shared by these two homology theories. In particular, we improve the bounds for the homological span of chromatic homology by Helme-Guizon, Przy…
We generalize the construction of the Heegaard Floer homology for a singular knot to that for a balanced bipartite graph. For a given graph, we provide a combinatorial description of the Euler characteristic of its Heegaard Floer homology by using the "Kauffman states" on a graph diagram.
New homology theory for graphs detects subdivisions and homology manifolds.
Graph manifolds with small homology have non-trivial SU(2) representations.
Proves Khovanov homology has no torsion for bipartite circle graphs.
We define Khovanov homology mod 2 for graph-links.
The paper calculates asymptotic Betti numbers and homology multiplicities for graph configuration spaces.
The article uses PageRank and persistent homology for scalable graph comparison.
Researchers determined the second homology group of a specific symplectic derivation Lie algebra.
We construct maps on hat Heegaard Floer homology for cobordisms decorated with graphs. The graph TQFT allows for cobordisms with disconnected ends. Our construction uses Juhász's sutured Floer TQFT. We compute the maps for several elementary graph cobordisms. As an application, we compute the action of the fundamental …
This paper defines girth for knots and links, linking it to Khovanov homology.
Kronheimer-Mrowka's instanton homology dimension equals Tait colorings.
We define integral odd Khovanov homology of principally unimodular bipartite graph-links.
We show that a graph manifold which is a Z-homology 3-sphere not homeomorphic to either the 3-sphere or the Poincaré homology 3-sphere admits a horizontal foliation. This combines with known results to show that the conditions of not being an L-space, of having a left-orderable fundamental group, and of admitting a co-…
Characterizes a specific homology group for certain graphs.
We show that Khovanov homology and Hochschild homology theories share common structure. In fact they overlap: Khovanov homology of a -torus link can be interpreted as a Hochschild homology of the algebra underlining the Khovanov homology. In the classical case of Khovanov homology we prove the concrete connectio…
The SO(3) Kauffman polynomial and the chromatic polynomial of planar graphs are categorified by a unique extension of the Khovanov homology framework. Many structural observations and computations of homologies of knots and spin networks are included.
Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram , there is an associated ribbon graph whose quasi-trees correspond bijectively to …
We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of homological properties of the graphs. We use our results to construct algebras wit…
The homology of Kontsevich's commutative graph complex parameterizes finite type invariants of odd dimensional manifolds. This {\it graph homology} is also the twisted homology of Outer Space modulo its boundary, so gives a nice point of contact between geometric group theory and quantum topology. In this paper we give…
Study Brieskorn spheres using Floer homology, generating infinite rank summands in homology cobordism.
New TQFT homologies help color graphs, potentially solving the four color theorem.
We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsváth and Szabó's TQFT for closed and connected 3-manifolds, and allows for cobordisms with disconnected ends. As an application, we give an explicit formula for the chain homotopy type of the -action on Heegaard Fl…
A graph multilink is a link with multiplicities in a homology 3-sphere whose exterior is a graph manifold. In this Note, we compute the Novikov homology of graph multilinks. As a corollary, we give a majoration for the number of Novikov modules on a given graph link.
Study semi-coarse spaces' homotopy and homology, extending coarse geometry.
Study supports conjecture about pretzel links' homology.
New graph kernel for weighted directed networks using functor homology.
Constructs homologies for ribbon graphs to recover Penrose polynomials.
In analogy with a recursive formula for the HOMFLY-PT polynomial of links given by Jaeger, we give a recursive formula for the graph polynomial introduced by Kauffman and Vogel. We show how this formula extends to the Khovanov-Rozansky graph homology.
We show that the knot lattice homology of a knot in an L-space is equivalent to the knot Floer homology of the same knot (viewed these invariants as filtered chain complexes over the polynomial ring Z/2Z [U]). Suppose that G is a negative definite plumbing tree which contains a vertex w such that G-w is a union of rati…