Results 1  10
of
48
Hénon mappings in the complex domain. II. Projective and inductive limits of polynomials. Real and complex dynamical systems
, 1995
"... Abstract. Let H: C 2 → C 2 be the Hénon mapping given by ..."
Abstract

Cited by 26 (6 self)
 Add to MetaCart
Abstract. Let H: C 2 → C 2 be the Hénon mapping given by
Homological stability for the mapping class groups of nonorientable surfaces
, 2007
"... We prove that the homology of the mapping class groups of nonorientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable mapping class group of nonorientable surfaces, up to homology is ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
We prove that the homology of the mapping class groups of nonorientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable mapping class group of nonorientable surfaces, up to homology isomorphism, is the infinite loop space of a Thom spectrum built from the canonical bundle over the Grassmannians of 2planes in R n+2. In particular, we show that the stable rational cohomology is a polynomial algebra on generators in degrees 4i—this is the nonoriented analogue of the Mumford conjecture.
MAPPING CLASS GROUP DYNAMICS ON SURFACE GROUP REPRESENTATIONS
"... Abstract. Deformation spaces Hom(π,G)/G of representations of the fundamental group π of a surface Σ in a Lie group G admit natural actions of the mapping class group ModΣ, preserving a Poisson structure. When G is compact, the actions are ergodic. In contrast if G is noncompact semisimple, the asso ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
Abstract. Deformation spaces Hom(π,G)/G of representations of the fundamental group π of a surface Σ in a Lie group G admit natural actions of the mapping class group ModΣ, preserving a Poisson structure. When G is compact, the actions are ergodic. In contrast if G is noncompact semisimple, the associated deformation space contains open subsets containing the FrickeTeichmüller space upon which ModΣ acts properly. Properness of the ModΣaction relates to (possibly singular) locally homogeneous geometric structures on Σ. We summarize known results and state open questions about these actions.
GENERATING FUNCTIONAL IN CFT AND EFFECTIVE ACTION FOR TWODIMENSIONAL QUANTUM GRAVITY ON HIGHER GENUS RIEMANN SURFACES
, 1996
"... We formulate and solve the analog of the universal Conformal Ward Identity for the stressenergy tensor on a compact Riemann surface of genus g> 1, and present a rigorous invariant formulation of the chiral sector in the induced twodimensional gravity on higher genus Riemann surfaces. Our construc ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
We formulate and solve the analog of the universal Conformal Ward Identity for the stressenergy tensor on a compact Riemann surface of genus g> 1, and present a rigorous invariant formulation of the chiral sector in the induced twodimensional gravity on higher genus Riemann surfaces. Our construction of the action functional uses various double complexes naturally associated with a Riemann surface, with computations that are quite similar to descent calculations in BRST cohomology theory. We also provide an interpretation of the action functional in terms of the geometry of different fiber spaces over the Teichmüller space of compact Riemann surfaces of genus g> 1.
Homology stability of nonorientable mapping class groups with marked points
 Proc. Amer. Math. Soc
"... Abstract. Wahl recently proved that the homology of the nonorientable mapping class group stabilizes as the genus increases. In this short note we analyse the situation where the underlying nonorientable surfaces have marked points. 1. ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Abstract. Wahl recently proved that the homology of the nonorientable mapping class group stabilizes as the genus increases. In this short note we analyse the situation where the underlying nonorientable surfaces have marked points. 1.
AREA DEPENDENCE IN GAUGED GROMOVWITTEN THEORY
"... Abstract. We study the variation of the moduli space of symplectic vortices on a fixed holomorphic curve with respect to the area form. For compact, convex varieties we define symplectic vortex invariants and prove a wallcrossing formula for them. As an application, we prove a vortex version of the ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract. We study the variation of the moduli space of symplectic vortices on a fixed holomorphic curve with respect to the area form. For compact, convex varieties we define symplectic vortex invariants and prove a wallcrossing formula for them. As an application, we prove a vortex version of the abelianization conjecture of Bertram, CiocanFontanine, and Kim [4], which related GromovWitten invariants of geometric invariant theory quotients by a group and its maximal torus, for vortices on nontrivial bundles.
CONSTRAINED WILLMORE SURFACES
, 2004
"... Abstract. The aim of this article is to develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ H 2 dA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is in ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
Abstract. The aim of this article is to develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ H 2 dA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surfaces in space forms. 1.
FROM MAPPING CLASS GROUPS TO AUTOMORPHISM GROUPS OF FREE GROUPS
, 2005
"... It is shown that the natural map from the mapping class groups of surfaces to the automorphism groups of free groups induces an infinite loop map on the classifying spaces of the stable groups after plus construction. The proof uses automorphisms of free groups with boundaries which play the role of ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
It is shown that the natural map from the mapping class groups of surfaces to the automorphism groups of free groups induces an infinite loop map on the classifying spaces of the stable groups after plus construction. The proof uses automorphisms of free groups with boundaries which play the role of mapping class groups of surfaces with several boundary components.
The stable mapping class group and stable homotopy theory
 EUROPEAN CONGRESS OF MATHEMATICS, 283–307, EUR. MATH. SOC
, 2005
"... This overview is intended as a lightweight companion to the long article [20]. One of the main results there is the determination of the rational cohomology of the stable mapping class group, in agreement with the Mumford conjecture [26]. This is part of a recent development in surface theory which ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This overview is intended as a lightweight companion to the long article [20]. One of the main results there is the determination of the rational cohomology of the stable mapping class group, in agreement with the Mumford conjecture [26]. This is part of a recent development in surface theory which was set in motion by Ulrike Tillmann’s discovery [34] that Quillen’s plus construction turns the classifying space of the stable mapping class group into an infinite loop space. Tillmann’s discovery depends heavily on Harer’s homological stability theorem [15] for mapping class groups, which can be regarded as one of the high points of geometric surface theory.
Framed bordism and lagrangian embeddings of exotic spheres
, 2008
"... 2. Construction of the bounding manifold 3 3. Transversality 21 4. Preliminaries for gluing 28 ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
2. Construction of the bounding manifold 3 3. Transversality 21 4. Preliminaries for gluing 28