𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Stein 4-manifolds with boundary and contact structures

✍ Scribed by P. Lisca; G. Matić

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
628 KB
Volume
88
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

We discuss several applications of Seiberg-Witten theory in conjunction with an embedding theorem (proved elsewhere) for complex 2-dimensional Stein manifolds with boundary. We show that a closed, real 2-dimensional surface smoothly embedded in the interior of such a manifold satisfies an adjunction inequality, regardless of the sign of its self-intersection. This inequality gives constraints on the minimum genus of a smooth surface representing a given 2-homology class. We also discuss consequences for the contact structures existing on the boundaries of these Stein manifolds. We prove a slice version of the Bennequin-Eliashberg inequality for holomorphically tillable contact structures, and we show that there exist families of homology 3-spheres with arbitrarily large numbers of homotopic, nonisomorphic tight contact structures. Another result we mention is that the canonical class of a complex 2-dimensional Stein manifold with boundary is invariant under self-diffeomorphisms fixing the boundary.

📜 SIMILAR VOLUMES

Theorem B for Stein Manifolds with Stric
Theorem B for Stein Manifolds with Strictly Pseudoconvex Boundary
✍ Dieter Heunemann 📂 Article 📅 1986 🏛 John Wiley and Sons 🌐 English ⚖ 735 KB

Let D c c C\* be strictly pseudoconvex, let aD be the boundary of D, and let 8 := D u aD. There are many papers where the $-equation af = g on 8 is investigated with respect to the behaviour of the solution near the boundary depending on the bouudary properties of g. We give some of these results wh

Quantization and contact structure on ma
Quantization and contact structure on manifolds with projective structure
✍ Indranil Biswas; Rukmini Dey 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 134 KB

We consider complex manifolds with a class of holomorphic coordinate functions satisfying the condition that each transition function is given by the standard action on CP 2n-1 of some element in Sp(2n, C)/Z 2 . We show that such a manifold has a natural contact structure. Given any contact manifold

Embedding 3-manifolds and smooth structu
Embedding 3-manifolds and smooth structures of 4-manifolds
✍ Fang Fuquan 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 719 KB

Let M be a noncompact 4-manifold with at least two open ends. Suppose that one of these ends is homeomorphic to N x iI& where N is an oriented 3-manifold satisfying one of the following conditions: (i) ~1 (N) is an extension of the free group by a perfect normal subgroup. (ii) HI (N) g Z/n, @. @ Z

Meromorphic symbolic structures for boun
Meromorphic symbolic structures for boundary value problems on manifolds with edges
✍ G. De Donno; B.-W. Schulze 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 431 KB

## Abstract We investigate the ideal of Green and Mellin operators with asymptotics for a manifold with edge‐corner singularities and boundary which belongs to the structure of parametrices of elliptic boundary value problems on a configuration with corners whose base manifolds have edges. (© 2006