arXiv research

Study circle actions on unitary manifolds with discrete fixed points.

The paper confirms a conjecture about compact unitary manifolds with non-empty fixed points.

The paper proves that a specific manifold is unitary cobordant to S^2 × S^6.

The study shows ergodicity of unitary frame flows on Kähler manifolds with specific curvature conditions.

We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle. We also classify such representations under a certain condition. The number of the equivalence…

We show that a unipotent vector bundle on a non-Kaehler compact complex manifold does not admit a flat holomorphic connection in general. We also construct examples of topologically trivial stable vector bundle on compact Gauduchon manifold that does not admit any unitary flat connection.

Spin-harmonic structures on low-dimensional manifolds.

Zeta functions for non-unitary twists are shown to have analytic continuation.

Given two unitary involutions $σ_{1}$ and $σ_{2}$ satisfying $G σ_{i} = - σ_{i} G$ on $ker B$ on a compact manifold with cylindrical end, M. Lesch, K. Wojciechowski ([LW]) and W. Müller ([M]) established the formula describing the difference of two eta-invariants with the APS boundary conditions associated with $σ_{1}$…

Main Theorem (3.3): Let $M$ be a compact four-dimensional manifold either with curvature, positive on complex isotropic two-planes, or self-dual of positive scalar curvature. If $π_1 (M)$ admits a nontrivial unitary representation, and $M$ is orientable, then there exists a surjective homomorphism from $π_1 (M)$ on $\b…

We construct a 2+1 dimensional classical gauge theory on manifolds with spin structure whose action is a refinement of the Atiyah-Patodi- Singer eta-invariant for twisted Dirac operators. We investigate the properties of the Lagrangian field theory for closed, spun 3-manifolds and compact, spun 3-manifolds with boundar…

In 1974, Berezin proposed a quantum theory for dynamical systems having a Kähler manifold as their phase space. The system states were represented by holomorphic functions on the manifold. For any homogeneous Kähler manifold, the Lie algebra of its group of motions may be represented either by holomorphic differential …

The paper bounds Betti numbers of complex-hyperbolic manifolds.

Paper proves non-compact inaudibility of symmetry and commutativity.

Study of unitary and groupoid orbits of normal operators, focusing on manifold structures and spectral conditions.

Let L->M be a Hermitian line bundle over a compact manifold. Write S for the space of all unitary connections in L whose curvatures define symplectic forms on M and G for the group of unitary bundle isometries of L, which acts on S by pull-back. The main observation of this note is that S carries a G-invariant symplect…

We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We also construct a family of special unitary quasitoric manifolds which contains polynomial gen…

Constructs a Morse-Bott function on symplectic Grassmannians.

Let $U_c(H)={u: u is unitary and u-1 is compact}$ stand for the unitary Fredholm group. We prove the following convexity result. Denote by $d_\infty$ the rectifiable distance induced by the Finsler metric given by the operator norm in $U_c(H)$. If $u_0,u_1,u\in U_c(H)$ and the geodesic $β$ joining $u_0$ and $u_1$ in $U…

Paper proves naturally reductive property is inaudible for certain manifolds.

We construct new proper biharmonic functions defined on open and dense subsets of the special unitary group SU(2). Then we employ a duality principle to obtain new proper biharmonic functions from the non-compact 3-dimensional hyperbolic space H^3.

Explicit pseudo-Kähler metrics on flag manifolds are described.

New unitary representations for mapping class groups without almost invariant vectors.

Study on determinants of unitary Brownian motion and their asymptotic laws.

In this work we wish characterize the Einstein manifolds $(M,g)$, however without the necessity of hypothesis of compactness over $M$ and unitary volume of $g$, which are well known in many works. Our result says that if all eingenvalues $λ$ of $r_{g}$, with respect to $g$, satisfy $λ\geq \frac{1}{n}s_{g}$, then $(M,g)…

Using Morse-theoretic techniques, we show that the moduli space of U*(2n)-Higgs bundles over a compact Riemann surface is connected.

Affirmatively answers Kosniowski conjecture for unitary S^1-manifolds.

Random matrix ensembles yield uniform distributions on manifolds.

New biharmonic functions created on Lie groups.

The study finds invariant Einstein metrics on complex Stiefel manifolds and special unitary groups.

We establish a Hard Lefschetz Theorem for the de Rham cohomology of compact Vaisman manifolds. A similar result is proved for the basic cohomology with respect to the Lee vector field. Motivated by these results, we introduce the notions of a Lefschetz and of a basic Lefschetz locally conformal symplectic (l.c.s.) mani…

Minimal energy local systems on curves are compact components of character varieties.

The study extends a theorem to bundles on manifolds with boundaries.

Unified study of surfaces using Clifford algebras.

New method solves $KP$ problem using global Cartan decompositions.

Convexity proven for sums of angles of unitary paths.

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that the possible singularities of this variety as well as of the corresponding modul…

Paper uses Turaev-Viro TQFT to estimate 3-manifold genus.

The goal of this diploma thesis is to give a detailed description of Kirillov's Orbit Method for the case of compact connected Lie groups. The theory of Kirillov aims at finding all irreducible unitary representations of a given Lie group $G$. The first chapter is intended to recall some facts about Lie groups. The mos…

Minimal dimensions found for flag manifolds embeddings.

This is a short version of math.DG/0505537. For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an…

We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then apply our method to construct many examples of compact minimal submanifolds of the special u…

Holomorphic Higgs bundles on Teichmüller space for surface groups.

New formula connects surface singularity zeta function to Reidemeister-Turaev torsion.

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE). Deviating from the standard "supersymmetry" approach, we integrate out Grassmann …

This article provides an account of the functorial correspondence between irreducible singular $G$-monopoles on $S^1\times Σ$ and $\vec{t}$-stable meromorphic pairs on $Σ$. The main theorem of [1] is thus generalized here from unitary to arbitrary compact, connected gauge groups. The required distinctions and similarit…

The paper analyzes the spectra of compact quotients of the oscillator group.

For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an analytic counterpart of the refined combina…