Topology of surface diagrams of smooth 4-manifolds.
نویسنده
چکیده
Surface diagrams are a new way to specify any smooth closed orientable 4-manifold by an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each curve has a unique transverse intersection with the next. The aim of this paper is to announce a uniqueness theorem for these objects (within a fixed homotopy class) that turns out to be similar to the Reidemeister-Singer theorem for Heegaard splittings of 3-manifolds.
منابع مشابه
A Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملSymplectic Rational Blowdowns
We prove that the rational blowdown, a surgery on smooth 4-manifolds introduced by Fintushel and Stern, can be performed in the symplectic category. As a consequence, interesting families of smooth 4-manifolds, including the exotic K3 surfaces of Gompf and Mrowka, admit symplectic structures. A basic problem in symplectic topology is to understand what smooth manifolds admit a symplectic struct...
متن کاملFour dimensions from two in symplectic topology
This paper introduces two-dimensional diagrams that are slight generalizations of moment map images for toric four-manifolds and catalogs techniques for reading topological and symplectic properties of a symplectic four-manifold from these diagrams. The paper offers a purely topological approach to toric manifolds as well as methods for visualizing other manifolds, including the K3 surface, and...
متن کاملLinks, Two-handles, and Four-manifolds
We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth cobordisms between two given closed 3-manifolds. As a consequence, there are finitely many smooth closed 4-manifolds constructed from some Kirby diagram with bou...
متن کاملRochlin’s theorem on signatures of spin 4-manifolds via algebraic topology
We give the original proof of Rochlin’s famous theorem on signatures of smooth spin 4-manifolds, which uses techniques from algebraic topology. We have attempted to include enough background and details to make this proof understandable to a geometrically minded topologist. We also include a fairly complete discussion of spin structures on manifolds.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 108 20 شماره
صفحات -
تاریخ انتشار 2011