scholarly journals Zariski Density of Monodromy Groups via a Picard–Lefschetz Type Formula

2017 ◽  
Vol 2018 (11) ◽  
pp. 3556-3586
Author(s):  
Jinxing Xu
Keyword(s):  
Type Formula ◽  
Lefschetz Type ◽  
Monodromy Groups

Algebraic torsion, zeta function and Dirichlet series for graph links in homology 3-spheres

1993 ◽  
Vol 13 (1) ◽  
pp. 131-142
Author(s):  
András Némethi
Keyword(s):  
Dynamical System ◽  
Topological Space ◽  
Zeta Function ◽  
Dirichlet Series ◽  
Ring Homomorphism ◽  
Fiber Structure ◽  
Product Decomposition ◽  
Type Formula ◽  
Lefschetz Type ◽  
Splice Diagram

AbstractIn this paper, we define the algebraic torsion τ associated with an -constructible sheaf ℱ on a topological space X and a ring homomorphism π1(X) → Z (with an acyclicity condition). If (X, ) has a fiber structure over S1, then τ is equal to the zeta function of the monodromy acting on the hypercohomology of the fiber. If X is the complement of a link in a homology 3-sphere and is given by a link such that admits a fiberable splice diagram, then this zeta function has a product decomposition (corresponding to the Jaco-Shalen-Johansson decomposition). This can be interpreted as a ‘Lefschetz type formula’ for a dynamical system suitably chosen.

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

scholarly journals Independence of algebraic monodromy groups in compatible systems

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Federico Amadio Guidi
Keyword(s):  
Galois Representations ◽  
Global Function ◽  
Irreducible Decomposition ◽  
Global Function Fields ◽  
Normal Varieties ◽  
Independence Result ◽  
Monodromy Groups ◽  
Independence Results ◽  
Lisse Sheaves ◽  
General Method

AbstractIn this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in positive characteristic settings. In the abstract case, we prove an independence result for compatible systems of Lie-irreducible representations, from which we deduce an independence result for compatible systems admitting what we call a Lie-irreducible decomposition. In the case of geometric compatible systems of Galois representations arising from certain classes of automorphic forms, we prove the existence of a Lie-irreducible decomposition. From this we deduce an independence result. We conclude with the case of compatible systems of Galois representations over global function fields, for which we prove the existence of a Lie-irreducible decomposition, and we deduce an independence result. From this we also deduce an independence result for compatible systems of lisse sheaves on normal varieties over finite fields.

scholarly journals Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

2021 ◽  
Author(s):  
Andreas Bernig ◽  
Dmitry Faifman ◽  
Gil Solanes
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Riemannian Space ◽  
Space Forms ◽  
Type Formula ◽  
Isometric Embeddings ◽  
Curvature Measures ◽  
Riemannian Space Forms

AbstractThe recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

SPACE-CHARGE LAYER, INTRINSIC "BULK" AND SURFACE COMPLEX DEFECTS IN ZnO NANOPARTICLES — A HIGH-FIELD ELECTRON PARAMAGNETIC RESONANCE ANALYSIS

2013 ◽  
Vol 06 (04) ◽  
pp. 1330004 ◽  
Author(s):  
RÜDIGER-A. EICHEL ◽  
EMRE ERDEM ◽  
PETER JAKES ◽  
ANDREW OZAROWSKI ◽  
JOHAN VAN TOL ◽  
...  
Keyword(s):  
Electron Paramagnetic Resonance ◽  
Space Charge ◽  
Zno Nanoparticles ◽  
High Field ◽  
Space Charge Layer ◽  
Paramagnetic Resonance ◽  
Charge Layer ◽  
Type Formula ◽  
Field Electron ◽  
Electron Paramagnetic

The defect structure of ZnO nanoparticles is characterized by means of high-field electron paramagnetic resonance (EPR) spectroscopy. Different point and complex defects could be identified, located at the "bulk" or the surface region of the nanoparticles. In particular, by exploiting the enhanced g-value resolution at a Larmor frequency of 406.4 GHz, it could be shown that the resonance commonly observed at g = 1.96 is comprised of several overlapping resonances from different defects. Based on the high-field EPR analysis, the development of a space-charge layer could be monitored that consists of (shallow) donor-type [Formula: see text] defects at the "bulk" and acceptor-type [Formula: see text] and complex [Formula: see text] defects at the surface. Application of a core-shell model allows to determine the thickness of the depletion layer to 1.0 nm for the here studied compounds [J.J. Schneider et al., Chem. Mater.22, 2203 (2010)].

Quantum Homomorphisms of Associative Algebras

1997 ◽  
Vol 12 (38) ◽  
pp. 2963-2974
Author(s):  
A. E. F. Djemai
Keyword(s):  
Quantum Group ◽  
Associative Algebra ◽  
Associative Algebras ◽  
Type Formula ◽  
Algebra Of Functions ◽  
Inhomogeneous Quantum

Given an associative algebra A generated by {ek, k=1, 2,…} and with an internal law of type: [Formula: see text], we first show that it is possible to construct a quantum bi-algebra [Formula: see text] with unit and generated by (non-necessarily commutative) elements [Formula: see text] satisfying the relations: [Formula: see text]. This leads one to define a quantum homomorphism[Formula: see text]. We then treat the example of the algebra of functions on a set of N elements and we show, for the case N=2, that the resulting bihyphen;algebra is an inhomogeneous quantum group. We think that this method can be used to construct quantum inhomogeneous groups.

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