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.
The paper sets lower bounds for a Kirby-Thompson invariant of 4-manifolds.
New 4-manifold invariant defined from trisection diagrams.
Invariants for 4-manifolds from Hopf group-algebras.
We construct an invariant of closed 4-manifolds using families of Seiberg-Witten equations. This invariant is formulated as a cohomology class on a certain abstract simplicial complex consisting of embedded surfaces of a 4-manifold. We also give examples of 4-manifolds which admit positive scalar curvatu…
Detects exotic embeddings in 4-manifolds with boundary.
This paper constructs exotic diffeomorphisms on reducible 4-manifolds with odd b+.
The broken genera are orientation preserving diffeomorphism invariants of closed oriented 4-manifolds, defined via broken Lefschetz fibrations. We study the properties of the broken genera invariants, and calculate them for various 4-manifolds, while showing that the invariants are sensitive to exotic smooth structures…
The study sets constraints on 4-manifold forms linked to specific invariants.
New invariant for classifying 4-manifolds up to cobordism.
We give formulae for the Ozsvath-Szabo invariants of 4-manifolds X obtained by fiber sum of two manifolds M_1, M_2 along surfaces S_1, S_2 having trivial normal bundle and genus g>0. The formulae follow from a general theorem on the Ozsvath-Szabo invariants of the result of gluing two 4-manifolds along a common boundar…
New criterion for almost-complex 4-manifolds using polyhedral decompositions.
We define a diffeomorphism invariant of smooth 4-manifolds which we can estimate for many smoothings of R^4 and other smooth 4-manifolds. Using this invariant we can show that uncountably many smoothings of R^4 support no Stein structure. (Gompf has constructed uncountably many smoothings of R^4 which do support Stein …
New invariants derived from link homology for 4-manifolds.
New method classifies spin 4-manifolds using Kervaire-Milnor invariant.
The study examines the realizability of a 4-manifold invariant for homeomorphisms.
The main result of this paper is a formula for calculating the Seiberg-Witten invariants of 4-manifolds with fixed-point free circle actions. This is done by showing under suitable conditions the existence of a diffeomorphism between the moduli space of the 4-manifold and the moduli space of the quotient 3-orbifold. Tw…
The Kuperberg invariant is a topological invariant of closed 3-manifolds based on finite-dimensional Hopf algebras. In this paper, we initiate the program of constructing 4-manifold invariants in the spirit of Kuperberg's 3-manifold invariant. We utilize a structure called a Hopf triplet, which consists of three Hopf a…
Formula calculates Seiberg-Witten invariants after surgery.
Involutory Hopf group-coalgebras provide new invariants for 4-manifold bundles.
Sum formula for relative Seiberg-Witten invariants in 4-manifolds.
New invariant calculates 4-manifolds using trisection diagrams and combings.
New constraints on embedded spheres and projective planes in 4-manifolds from Seiberg-Witten theory.
Proves simple type conjecture for mod 2 Seiberg-Witten invariants.
On a smooth closed oriented -manifold with a smooth action of a finite group on a Spin structure, -monopole invariant is defined by "counting" -invariant solutions of Seiberg-Witten equations for any -invariant Riemannian metric on . We compute -monopole invariants on some -manifolds. F…
We introduce an invariant of tuples of commutative diffeomorphisms on a 4-manifold using families of Seiberg-Witten equations. This is a generalization of Ruberman's invariant of diffeomorphisms defined using 1-parameter families of Seiberg-Witten equations. Our invariant yields an application to the homotopy groups of…
New inequality for links in 3D using 4D invariants.
We find the shape of the Donaldson invariants of a 4-manifold with b_1=0 and b^+>1, which may be not of simple type. The invariants appear as the q^0 coefficient of a expression given in terms of modular forms (as was predicted by Moore and Witten). We re-express the formula using complete elliptic integrals to prove a…
Study BF invariants using simple type concepts.
We introduce a diffeomorphism invariant of -manifolds, the -monopole invariant, defined by using the -monopole equations. We compute the invariants of several -manifolds, and prove gluing formulae. By using the invariants, we construct exotic smooth structures on the connecte…
Study cohomotopy classes for 4-manifolds using complex spin structures.
The abstract introduces a method to compute surface invariants in 4-manifolds.
Paper extends Miyazawa's construction to more 4-manifolds, finding exotic involutions and embeddings.
New invariant detects non-homotopy equivalent 4-manifolds.
New invariant for 4-manifolds with framed links, stronger than existing invariants.
We use a 1-parameter version of gauge theory to investigate the topology of the diffeomorphism group of 4-manifolds. A polynomial invariant, analogous to the Donaldson polynomial, is defined, and is used to show that the diffeomorphism group of certain simply-connected 4-manifolds has infinitely generated π_0.
The Hausmann-Weinberger invariant of a group G is the minimal Euler characteristic of a closed orientable 4-manifold M with fundamental group G. We compute this invariant for finitely generated free abelian groups and estimate the invariant for all finitely generated abelian groups.
Link homology theories connect to 4-manifold invariants and TQFTs.
A formula is given for the Seiberg-Witten invariants of a 4-manifold that is cut along certain kinds of 3-dimensional tori. The formula involves a Seiberg-Witten invariant for each of the resulting pieces.
Notes on Whitney towers in 4-manifolds, focusing on local surface manipulations and invariants.
The main results of this paper describes a formula for the Seiberg-Witten invariant of a 4-manifold which admits a nontrivial free S^1-action. We use this theorem to produce a nonsymplectic 4-manifold with a free circle action whose orbit space fibers over S^1. We also describe a 3-manifold which is not the orbit space…
The paper studies special crystallizations of 4-manifolds to minimize certain PL-invariants.
Proves surface embedding theorem for 4-manifolds with good fundamental group.
By using the gluing formulae of the Seiberg-Witten invariant, we show the nonexistence of Einstein metric on manifolds obtained from a 4-manifold with nontrivial Seiberg-Witten invariant by performing sufficiently many connected sums or appropriate surgeries along circles or homologically trivial 2-spheres with closed …
New proof shows exotic 4-manifolds exist without complex calculations.
We investigate the -monopole invariants of symplectic -manifolds and Kähler surfaces with real structures. We prove the nonvanishing theorem for real symplectic -manifolds which is an analogue of Taubes' nonvanishing theorem of the Seiberg-Witten invariants for symplectic -manifolds. Further…
New estimates are derived concerning the behavior of self-dual hamonic 2-forms on a compact Riemannian 4-manifold with non-trivial Seiberg-Witten invariants. Applications include a vanishing theorem for certain Seiberg-Witten invariants on compact 4-manifolds of constant negative sectional curvature.
We make use of -structures and technology developed by Paternain - Petean to compute minimal entropy, minimal volume, and Yamabe invariant of symplectic 4-manifolds, as well as to study their collapse with sectional curvature bounded from below. À la Gompf, we show that these invariants vanish on symplecti…
The goal of this paper is to demonstrate that, at least for nonsimply connected 4-manifolds, the Seiberg-Witten invariant alone does not determine diffeomorphism type within the same homeomorphism type.