Some Remarks on Degree Theory for So(2)-equivariant Transversal Maps
نویسندگان
چکیده
The aim of this article is to introduce a new class SO(2)equivariant transversal maps T R(cl(Ω), ∂Ω) and to define degree theory for such maps. We define degree for SO(2)-equivariant transversal maps and prove some properties of this invariant. Moreover, we characterize SO(2)-equivariant transversal isomorphisms and derive formula for degree of such isomorphisms.
منابع مشابه
Applications of Degree for S1-equivariant Gradient Maps to Variational Nonlinear Problems with S1-symmetries S
There are developed many topological methods which are powerful tools in the theory of critical points of functionals; see for example [2], [3], [5], [6], [9], [13]–[20], [22]–[25], [27]–[29], [32], [33], [43]–[45], [47], [48], [51], [59]. It happens quite often that functionals whose critical points are important in the theory of differential equations are invariant under an action of a compac...
متن کاملEquivariant maps between sphere bundles over tori and KO ∗ - degree
We show a non-existence result for some class of equivariant maps between sphere bundles over tori. The notion of equivariant KO *-degree is used in the proof. As an application we have an inequality b + 2 (X) ≥ −sign (X)/8 + c(X) + ε(X) for a 4-dimensional connected closed oriented spin manifold X whose intersection form is indefinite, where c(X) is a non-negative integer determined by the cup...
متن کاملSome remarks on the root invariant
We show how the root invariant of a product depends upon the product of the root invariants, give some examples of the equivariant definition of the root invariant, and verify a weakened form of the algebraic Bredon-Löffler conjecture . These remarks were worked out during the Stable Homotopy Theory Workshop at the Fields Institute in Toronto during January of 1996. The author would like to tha...
متن کاملResearch Plan
My current main project concerns the study of the interaction between the theory of operads and genuine equivariant homotopy theory. Briefly, an operad (introduced by May in [13]) consists of a sequence On of sets/spaces of “n-ary operations” together with Σn-actions and suitable compositions. The main point of operad theory is then the study of the algebras over a fixed operad O, which are o...
متن کاملQuasiconformal Homeomorphisms on Cr 3-manifolds with Symmetries
An extremal quasiconformal homeomorphisms in a class of homeomorphisms between two CR 3-manifolds is an one which has the least conformal distortion among this class. This paper studies extremal quasiconformal homeomorphisms between CR 3-manifolds which admit transversal CR circle actions. Equivariant K-quasiconformal homeomorphisms are characterized by an area-preserving property and the K-qua...
متن کامل