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.
Paper connects TQFTs and SKK invariants through a group homomorphism.
In this note we study the relative Kervaire semi-characteristic and prove its invariance under cut-and-past operation. Our approach is analytic and follow very closely the method introduced by W. Zhang
A simple method to create new 4-manifolds by altering fundamental groups.
New method recovers classical cut and paste groups for manifolds.
We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative inde…
The paper calculates Veech groups and Galois invariants for general origamis.
A new spectrum recovers cobordism cut and paste groups of manifolds with boundary.
In this paper, we will introduce a cut and paste move, called a geometrically null log transform, and prove that any two manifolds related by a sequence of these moves become diffeomorphic afte r one stabilization. To motivate the cut and paste move, we will use the symplec tic fiber sum, and a construction of Fintushe…
Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds; - the problem of cut-and-paste invariance of Novikov's higher signatures on closed manifolds; - the problem of defining higher signa…
Extends Penrose's method to null shells with pressure and energy flux.
Quantum Teichmüller invariants studied for 3-manifolds.
We derive a cut-and-paste surgery formula of Seiberg--Witten invariants for negative definite plumbed rational homology 3-spheres. It is similar to (and motivated by) Okuma's recursion formula [arXiv:math.AG/0610464, 4.5] targeting analytic invariants of splice quotient singularities. The two formulas combined provide …
We give a purely topological definition of the perturbative quantum invariants of links and 3-manifolds associated with Chern-Simons field theory. Our definition is as close as possible to one given by Kontsevich. We will also establish some basic properties of these invariants, in particular that they are universally …
These are lecture notes on cut-and-paste methods in 3-dimensional contact geometry.
For a certain class of compact oriented 3-manifolds, M. Goussarov and K. Habiro have conjectured that the information carried by finite-type invariants should be characterized in terms of ``cut-and-paste'' operations defined by the lower central series of the Torelli group of a surface. In this paper, we observe that t…
We extend the notion of the symmetric signature in L^n(R) for a compact n-dimensional manifold M without boundary, a reference map r from M to BG and a homomorphism of rings with involutions from ZG to R to the case with boundary , where is the …
Extends Milnor invariants to surface-links using cut-diagrams.
Teaches advanced differential topology to master students with minimal background.
We consider a left invariant Riemannian metric on SO(3) with two equal eigenvalues. We find the cut locus and the equation for the cut time. We find the diameter of such metric and describe the set of all most distant points from the identity. Also we prove that the cut locus and the cut time converge to the cut locus …
We calculate the eta-invariant for the odd signature operator relative to a specific submersion metric on the Milnor fibration of a quasihomogeneous hypersurface singularity using certain global boundary conditions in terms of the data of its fibre intersection form, monodromy and variation mapping resp. the monomial d…
Researchers develop a formula to calculate rho invariant of Dehn surgeries on links.
New classification of nonorientable 4-manifolds with specific fundamental groups.
Multisections generalize trisections for 4-manifolds, allowing complex operations and explicit diagrams.
New invariant defined for Weinstein domains, related to Kirby-Thompson's invariant.
Protocorks link exotic 4-manifolds, with applications to Floer homology.
We use quantum invariants to define a 3-manifold invariant j_p which lies in the non-negative integers. We relate j_p to the Heegard genus, and the cut number. We show that j_$ is an invariant of weak p-congruence.
This article is a follow up of the previous article of the authors on the analytic surgery of eta- and rho-invariants. We investigate in detail the (Atiyah-Patodi-Singer)-rho-invariant for manifolds with boundary. First we generalize the cut-and-paste formula to arbitrary boundary conditions. A priori the rho-invariant…
Invariants for surfaces with 0-, 1-, and 2-cells are derived from finite 2-groups.
This note provides an easy construction of fake octagons.
This work reviews left-invariant optimal control problems on Lie groups.
We introduce machinery to allow ``cut-and-paste''-style inductive arguments in the Torelli subgroup of the mapping class group. In the past these arguments have been problematic because restricting the Torelli group to subsurfaces gives different groups depending on how the subsurfaces are embedded. We define a categor…
We show that under appropriate hypotheses, a plumbing of symplectic surfaces in a symplectic 4-manifold admits strongly convex neighborhoods. Moreover the neighborhoods are Lefschetz fibered with an easily-described open book on the boundary supporting the induced contact structure. We point out some applications to cu…
Unified approach classifies stable and minimal elastic curves.
The paper confirms a conjecture and extends arrow polynomial to twisted links.
New equivalence relation for links using cut-diagrams.
In this paper we study the invariant Carnot-Caratheodory metrics on , and induced by their Cartan decomposition and by the Killing form. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory dis…
We prove for the Reidemeister-Turaev torsion of closed oriented three-manifolds some finiteness properties in the sense of Goussarov and Habiro, that is, with respect to some cut-and-paste operations which preserve the homology type of the manifolds. In general, those properties require the manifolds to come equipped w…
Study geodesics and metrics on PSL(2) group for hyperbolic plane.
New framework for sutured manifolds using handleslides and Heegaard invariants.
New upper bound for geodesic complexity derived from cut locus decompositions.
Bott and Taubes used integrals over configuration spaces to produce finite-type a.k.a. Vassiliev knot invariants. Cattaneo, Cotta-Ramusino and Longoni then used these methods together with graph cohomology to construct "Vassiliev classes" in the real cohomology of spaces of knots in higher-dimensional Euclidean spaces,…
We introduce the notion of a cut cellular surface (CCS), being a surface with boundary, which is cut in a specified way to be represented in the plane, and is composed of 0-, 1- and 2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular structure, by counting colourings of the 1-cells with elem…
We employ cut and paste contact topological techniques to classify some tight contact structures on the closed, oriented genus-2 surface times the interval. A boundary condition is specified so that the Euler class of the of the contact structure vanishes when evaluated on each boundary component. We prove that there e…
This is a survey of our program of perturbative quantization of gauge theories on manifolds with boundary compatible with cutting/pasting and with gauge symmetry treated by means of a cohomological resolution (Batalin-Vilkovisky) formalism. We also give two explicit quantum examples -- abelian BF theory and the Poisson…
Defines new link-homotopy invariants using Milnor's higher order link invariants.
Paper provides a performance guarantee for spectral clustering.
Proves bounds on spanning two-forests and random cut sizes.
New method to compute tangle sums in character varieties.