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An index inequality for embedded pseudoholomorphic curves in symplectizations

Michael Hutchings (2002)

Journal of the European Mathematical Society

Let Σ be a surface with a symplectic form, let φ be a symplectomorphism of Σ , and let Y be the mapping torus of φ . We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in ℝ × 𝕐 , with cylindrical ends asymptotic to periodic orbits of φ or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to understand...

An inequality for symplectic fillings of the link of a hypersurface K3 singularity

Hiroshi Ohta, Kaoru Ono (2009)

Banach Center Publications

Some relations between normal complex surface singularities and symplectic fillings of the links of the singularities are discussed. For a certain class of singularities of general type, which are called hypersurface K3 singularities in this paper, an inequality for numerical invariants of any minimal symplectic fillings of the links of the singularities is derived. This inequality can be regarded as a symplectic/contact analog of the 11/8-conjecture in 4-dimensional topology.

An introduction to gerbes on orbifolds

Ernesto Lupercio, Bernardo Uribe (2004)

Annales mathématiques Blaise Pascal

This paper is a gentle introduction to some recent results involving the theory of gerbes over orbifolds for topologists, geometers and physicists. We introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class, Beilinson-Deligne orbifold cohomology, Cheeger-Simons orbifold cohomology and string connections.

An o-minimal structure which does not admit C ∞ cellular decomposition

Olivier Le Gal, Jean-Philippe Rolin (2009)

Annales de l’institut Fourier

We present an example of an o-minimal structure which does not admit C ∞ cellular decomposition. To this end, we construct a function H whose germ at the origin admits a C k representative for each integer k , but no C ∞ representative. A number theoretic condition on the coefficients of the Taylor series of H then insures the quasianalyticity of some differential algebras 𝒜 n ( H ) induced by H . The o-minimality of the structure generated by H is deduced from this quasianalyticity property.

Anti-self-dual orbifolds with cyclic quotient singularities

Michael T. Lock, Jeff A. Viaclovsky (2015)

Journal of the European Mathematical Society

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation space of the Calderbank–Singer scalar-flat Kähler toric ALE spaces. A corollary of this is that, except for the Eguchi–Hanson metric, all of these spaces admit non-toric anti-self-dual deformations, thus yielding many new examples of anti-self-dual ALE spaces. For...

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