Related papers: Refined Seiberg-Witten invariants
This document is a reorganization of the results on the Master Thesis of the same title written by the author under the supervision of Dr. Christian Blohmann at the University of Bonn in 2014. There are three main results in this document.…
We study Betti structures in the solution complexes of confluent hypergeometric equations. We use the framework of enhanced ind-sheaves and the irregular Riemann-Hilbert correspondence of D'Agnolo-Kashiwara. The main result is a group…
We propose an abelian categorification of $\hat{Z}$-invariants for Seifert $3$-manifolds. First, we give a recursive combinatorial derivation of these $\hat{Z}$-invariants using graphs with certain hypercubic structures. Next, we consider…
We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants…
We introduce a notion of retraction between continuous maps of topological spaces and study the behavior of several numerical invariants under such retractions. These include (co)homological dimensions, the Lusternik-Schnirelmann category,…
We describe an effective algorithm for computing Seiberg-Witen invariants of lens spaces. We apply it to two problems: (i) to compute the Froyshov invariants of a large family of lens spaces; (ii) to show that the knowledge of the…
One of the main questions in the theory of normal surface singularities is to understand the relations between their geometry and topology. The lattice cohomology is an important tool in the study of topological properties of a plumbed…
We survey the progress on the study of symplectic geometry past five decades. The survey focuses on the convexity properties of a moment map, the classification of symplectic actions, the symplectic embedding problems, and the theory of…
A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category…
Given a three-manifold with b_1=1 and a nontorsion spin^c structure, we use finite dimensional approximation to construct from the Seiberg-Witten equations two invariants in the form of a periodic pro-spectra. Various functors applied to…
We construct infinite rank summands isomorphic to $\mathbb{Z}^\infty$ in the higher homotopy and homology groups of the diffeomorphism groups of certain $4$-manifolds. These spherical families become trivial in the homotopy and homology…
We introduce the weighted path homology on the category of weigh\-ted directed hypergraphs and describe conditions of homotopy invariance of weighted path homology groups. We give several examples that explain the nontriviality of the…
We develop a novel stability theory for Sinkhorn semigroups based on Lyapunov techniques and quantitative contraction coefficients, and establish exponential convergence of Sinkhorn iterations on weighted Banach spaces. This…
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with matter is analysed as an isomonodromy problem. We show that the holomorphic section describing the effective action can be deformed by moving its singularities on…
We discuss some exact Seiberg--Witten-type maps for noncommutative electrodynamics. Their implications for anomalies in different (noncommutative and commutative) descriptions are also analysed.
In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a…
We show a non-existence result for some class of equivariant maps between sphere bundles over tori. The notion of equivariant KO-degree is used in the proof. As an application to Seiberg-Witten theory, for a connected closed oriented spin…
We develop the Seiberg-Witten map using the gauge-covariant star product with the noncommutativity tensor $\theta^{\mu\nu}(x)$. The latter guarantees the Lorentz invariance of the theory. The usual form of this map and its other recent…
We present an approach to Gromov-Witten invariants that works on arbitrary (closed) symplectic manifolds. We avoid genericity arguments and take into account singular curves in the very formulation. The method is by first endowing mapping…