On the Genus of Smooth 4-manifolds
نویسنده
چکیده
The projective complex plane and the "twisted" S3 bundle over Sl are proved to be the unique closed prime connected (smooth or PL) 4-manifolds of genus two. Then the classification of the nonorientable 4-manifolds of genus 4 is given. Finally the genus of a manifold M is shown to be related with the 2nd Betti number of M and some applications are proved in the general (resp. simply-connected) case.
منابع مشابه
GROUPOID ASSOCIATED TO A SMOOTH MANIFOLD
In this paper, we introduce the structure of a groupoid associated to a vector field on a smooth manifold. We show that in the case of the $1$-dimensional manifolds, our groupoid has a smooth structure such that makes it into a Lie groupoid. Using this approach, we associated to every vector field an equivalence relation on the Lie algebra of all vector fields on the smooth...
متن کاملACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE
A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...
متن کاملMultiple point of self-transverse immesions of certain manifolds
In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...
متن کاملGEOMETRIZATION OF HEAT FLOW ON VOLUMETRICALLY ISOTHERMAL MANIFOLDS VIA THE RICCI FLOW
The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...
متن کاملCircle-sum and Minimal Genus Surfaces in Ruled 4-manifolds
We describe a circle-sum construction of smoothly embedded surface in a smooth 4-manifold. We apply this construction to give a simpler solution of the minimal genus problem for nontrivial S2 bundles over surfaces. We also treat the case of blow-ups.
متن کامل