Normal holomorphic curves from parabolic regions to projective spaces Alexandre Eremenko Spring 1998 Abstract A holomorphic map C !Pn is called normal if it is uniformly continuous from the Euclidean metric to the Fubini{Study metric The paper contains a survey of known results about such maps as well as some new theorems In this paper I give a completed topological characterization of Stein manifolds of complex dimension 2 Another paper (see [E14]) is devoted to new topogical obstructions for the existence of a Stein complex structure on real manifolds of dimension 4 Main

## Categorical representation and character theory

Spectral theory Theorem (After interpretation) 1 Character theory of topological G-representations is controlled by the (holomorphic) Lagrangian geometry of BFM(G_) 2 BFM(G_) is foliated by complete family of irreducible G-categories coming from the Toda integrable system 3 The G-representations 'are' the Gromov-Witten theories of G- ag varieties (Borel-Weil constru

Titles and Abstracts J E Andersen: Geometric recursion Abstract: We shall review the geometric recursion and its relation to topological recursion In particular we shall consider the target theory of continuous functions on Teichmller spaces and we shall exhibit a number of classes of mapping class group invariant functions which satisfies the geometric recursion

In the first talk I will present a holomorphic description of the limiting oper and its geometry The count of lattice points of the character variety ie representations from the fundamental group a punctured Riemann Surface to a finite group G is a 2D TQFT for the center of the group algebra of G

In mathematics a topological vector space (also called a linear topological space and commonly abbreviated TVS or t v s ) is one of the basic structures investigated in functional analysis A topological vector space is a vector space (an algebraic structure) which is also a topological space the latter thereby admitting a notion of continuity More specifically its topological space has a

Characterization of partial Hamiltonian operators and related first integrals Discrete Continuous Dynamical Systems - S 2018 11 (4) : 723-734 doi: 10 3934/dcdss 2018045 [4] Elena Celledoni Brynjulf Owren Preserving first integrals with symmetric Lie group methods

## 4 7 Topological Conjugacy and Equivalence

4 7 Topological Conjugacy and Equivalence Therefore the flows of linear systems on the parabola that have only a single eigenspace cannot be diffeomorphic to flows that have two eigenspaces In particular At there is a bifurcation a qualitative change in the character of the solution The

Inthis paper we prove that the negation of Gambaudo-P'ecou propertycharacterises the topological dynamics of holomorphic parabolic germs As aconsequence a rotation set for germs of surface homeomorphisms around a fixedpoint can be defined and it will turn out to be non trivial except forcountably many conjugacy classes

Spectral theory Theorem (After interpretation) 1 Character theory of topological G-representations is controlled by the (holomorphic) Lagrangian geometry of BFM(G_) 2 BFM(G_) is foliated by complete family of irreducible G-categories coming from the Toda integrable system 3 The G-representations 'are' the Gromov-Witten theories of G- ag varieties (Borel-Weil constru

Anti-holomorphic Fatou Coordinate Equator and Ecalle height Lemma Suppose z 0 is a parabolic periodic point of odd period of f c with only one petal and U is an immediate basin of attraction Then there exists a petal V ˆU and a univalent map : V !C conjugating the rst return map to z + 1 2 This map is unique up to horizontal translation

s: V !Wfrom one topological vectorspace to another is weakly holomorphic in a parameter s(in a connected complex manifold for example a connected open subset of C) if for every vector v2V and for every continuous functional 2W the C-valued function (T sv) is holomorphic in s In a di erent direction but likewise essential: [1 0 4] Proposition

The problem we address is to give a combinatorial characterization of the holomorphic maps contained in these classes whose post-singular sets are finite The main results in this paper are that a post-singularly finite topological exponential map of type $(0 1)$ or a certain post-singularly finite topological exponential map of type $(p 1)$ or

Marco Abate Iteration theory of holomorphic maps on taut manifolds Research and Lecture Notes in Mathematics Complex Analysis and Geometry Mediterranean Press Rende 1989 MR 1098711 Dov Aharonov Mark Elin Simeon Reich and David Shoikhet Parametric representations of semi-complete vector fields on the unit balls in 퐶ⁿ and in Hilbert space Atti Accad

2 Compacti cations as topological spaces 2 1 A uniform method for compacti cation [BJ] Let Y = nXbe a locally symmetric space as above Attach to Xcertain boundary components e(P) indexed by a -invariant collection Pof rational parabolic subgroups PˆG:The e(P) will be related to the Langlands

## //

For a smooth projective variety X the analytic index of a holomorphic vector bundle Vcan be deﬁned as the alternating sum ˜ XIV/of its sheaf cohomologies This agrees with the topological index of V deﬁned by the Gysin map to a point in topological K-theory The construction extends to certain well-behaved Artin stacks

We describe Borel–de Siebenthal representations by giving an algebraic characterization in terms of Lie algebra cohomology and a geometric characterization in terms of associated variety The theory of cohomological parabolic inductions developed by D A Vogan N R Wallach G J Zuckerman and others (cf Section 4 ) produces almost all

For a smooth projective variety X the analytic index of a holomorphic vector bundle Vcan be deﬁned as the alternating sum ˜ XIV/of its sheaf cohomologies This agrees with the topological index of V deﬁned by the Gysin map to a point in topological K-theory The construction extends to certain well-behaved Artin stacks

A HILBERT BUNDLE CHARACTERIZATION OF HILBERT C*-MODULES GEORGE A ELLIOTT AND KATSUNORI KAWAMURA Abstract The category of Hilbert C*-modules over a given C*-algebra is shown to be equivalent to a certain simply described category of Hilbert bun-dles (i e continuous ﬁelds of Hilbert spaces) over the space of pure states of

TOPOLOGICAL MODULI SPACE FOR GERMS OF HOLOMORPHIC FOLIATIONS DAVID MARN JEAN-FRANOIS MATTEI AND LIANE SALEM Abstract This work deals with the topological classiﬁcation of germs of singular foliations on (C2 0) Working in a suitable class of folia-tions we ﬁx the topological invariants given by the separatrix set the

parameterizing the rational maps gquasiconformal conjugate to f Corollary 2 5 If the Julia set of a rational map is the full sphere then the group Mod(Cb f) maps with ﬁnite kernel into a discrete subgroup of PSL 2(R)n⋉S n (the automorphism group of the polydisk) Proof The Teichmuller space of fis isomorphic to Hn Corollary 2 6 (Finiteness theorem) The number of cycles of stable

Deﬁnition 1 A unitary character χ of Nis said to be non-degenerate if dχ(Y) = iB(x Y) for Y ∈ θn and Ad(P)xis open in n In other words the orbit of xis a Richardson element in n C We note that there exist parabolic groups such that there are no such non-degenerate characters of