Uniform PL approximations of isotopies and extending PL isotopies in low dimensions
نویسندگان
چکیده
منابع مشابه
Definable isotopies
Let X be a definable C manifold, Y1, Y2 definably compact definable C r submanifolds of X such that dimY1 + dimY2 < dimX and Y1 has a trivial normal bundle. We prove that there exists a definable isotopy {hp}p∈J such that h0 = idX and h1(Y1) ∩ Y2 = ∅. 2010 Mathematics Subject Classification. 14P10, 14P20, 58A05, 03C64.
متن کاملLagrangian isotopies in Stein manifolds
Studying the space of Lagrangian submanifolds is a fundamental problem in symplectic topology. Lagrangian spheres appear naturally in the Leftschetz pencil picture of symplectic manifolds. In this paper we demonstrate the uniqueness up to Hamiltonian isotopy of the Lagrangian spheres in some 4-dimensional Stein symplectic manifolds. The most important example is the cotangent bundle of the 2-sp...
متن کاملFiber Quadrisecants in Knot Isotopies
Fix a straight line L in Euclidean 3-space and consider the fibration of the complement of L by half-planes. A generic knot K in the complement of L has neither fiber quadrisecants nor fiber extreme secants such that K touches the corresponding half-plane at 2 points. Both types of secants occur in generic isotopies of knots. We give lower bounds for the number of these fiber secants in all iso...
متن کاملGuiding Isotopies and Holomorphic Motions
We develop an isotopy principle for holomorphic motions. Our main result concerns the extendability of a holomorphic motion h(t, z) of a finite subset E of the Riemann sphere C parameterized by a pointed hyperbolic Riemann surface (X, t0). We prove that if this holomorphic motion has a guiding quasiconformal isotopy, then it can be extended to a new holomorphic motion of E ∪ {p} for any point p...
متن کاملPositive isotopies of Legendrian submanifolds and applications
We show that there is no positive loop inside the component of a fiber in the space of Legendrian embeddings in the contact manifold ST ∗M , provided that the universal cover of M is Rn. We consider some related results in the space of one-jets of functions on a compact manifold. We give an application to the positive isotopies in homogeneous neighborhoods of surfaces in a tight contact 3-manif...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1976
ISSN: 0001-8708
DOI: 10.1016/0001-8708(76)90020-7