On Symmetric Group S3 Actions on Spin 4-manifolds
نویسندگان
چکیده
Let X be a smooth, closed, connected spin 4-manifold with b1(X) = 0 and non-positive signature σ(X). In this paper we use Seiberg-Witten theory to prove that if X admits an odd type symmetric group S3 action preserving the spin structure, then b+2 (X) ≥ |σ(X)|/8 + 3 under some non-degeneracy conditions. We also obtain some information about IndS̃3 D, where S̃3 is the extension of S3 by Z2.
منابع مشابه
On Lorentzian two-Symmetric Manifolds of Dimension-four
‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎.
متن کاملPositivity of relativistic spin network evaluations
LetG be a compact Lie group. Using suitable normalization conventions, we show that the evaluation of G×G-symmetric spin networks is non-negative whenever the edges are labeled by representations of the form V ⊗ V ∗ where V is a representation of G, and the intertwiners are generalizations of the Barrett–Crane intertwiner. This includes in particular the relativistic spin networks with symmetry...
متن کاملCircle Actions on Homotopy Spheres Not Bounding Spin Manifolds
Smooth circle actions are constructed on odd-dimensional homotopy spheres that do not bound spin manifolds. Examples are given in every dimension for which exotic spheres of the described type exist. A result of H. B. Lawson and S.-T. Yau [15] implies that homotopy spheres not bounding spin manifolds do not admit effective smooth S3 or S03 actions. On the other hand, G. Bredon has shown that ev...
متن کاملOn $(epsilon)$ - Lorentzian para-Sasakian Manifolds
The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.
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 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:
دوره شماره
صفحات -
تاریخ انتشار 2007