Submanifolds, group actions and knots. I
نویسندگان
چکیده
منابع مشابه
Submanifolds , Group Actions and Knots . I
This note and [4] outline new methods of classifying submanifolds of a manifold, submanifolds invariant under a group action, and submanifolds fixed under a group action. These methods solve many previously difficult problems associated with codimension two. In particular, they lead to a better understanding of the role of knot theory in the general placement problem for manifolds; this will be...
متن کاملAlmost Invariant Submanifolds for Compact Group Actions
A compact (not necessarily connected) Lie group G carries a (unique) biinvariant probability measure. Using this measure, one can average orbits of actions of G on affine convex sets to obtain fixed points. In particular, if G acts on a manifoldM , G leaves invariant a riemannian metric onM , and this metric can sometimes be used to obtain fixed points for the nonlinear action of G on M itself....
متن کاملNormal Forms for Submanifolds under Group Actions
We describe computational algorithms for constructing the explicit power series expansions for normal forms of submanifolds under transformation groups. The procedure used to derive the coefficients relies on the recurrence formulae for differential invariants provided by the method of equivariant moving frames.
متن کاملHamiltonian Actions and Homogeneous Lagrangian Submanifolds
We consider a connected symplectic manifold M acted on properly and in a Hamiltonian fashion by a connected Lie group G. Inspired to the recent paper [3], see also [12] and [24], we study Lagrangian orbits of Hamiltonian actions. The dimension of the moduli space of the Lagrangian orbits is given and we also describe under which condition a Lagrangian orbit is isolated. If M is a compact Kähler...
متن کاملGROUP ACTIONS ON SPIN MANIFOLDS(i)
A generalization of the theorem of V. Bargmann concerning unitary and ray representations is obtained and is applied to the general problem of lifting group actions associated to the extension of structure of a bundle. In particular this is applied to the Poincare group ? of a Lorentz manifold M. It is shown that the topological restrictions needed to lift an action in ? are more stringent than...
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: Bulletin of the American Mathematical Society
سال: 1972
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1972-13103-3