The Burnside Ring-valued Morse Formula for Vector Fields on Manifolds with Boundary
نویسنده
چکیده
Let G be a compact Lie group and A(G) its Burnside Ring. For a compact smooth n-dimensional G-manifold X equipped with a generic Ginvariant vector field v, we prove an equivariant analog of the Morse formula Ind(v) = n
منابع مشابه
Bilateral composition operators on vector-valued Hardy spaces
Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$. We investigate some operator theoretic properties of bilateral composition operator $C_{ph, T}: f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq +infty$. Compactness and weak compactness of $C_{ph, T}$ on $H^p(X)$ are characterized an...
متن کاملMorse’s index formula in VMO for compact manifolds with boundary
In this paper, we study Vanishing Mean Oscillation vector fields on a compact manifold with boundary. Inspired by the work of Brezis and Niremberg, we construct a topological invariant — the index — for such fields, and establish the analogue of Morse’s formula. As a consequence, we characterize the set of boundary data which can be extended to nowhere vanishing VMO vector fields. Finally, we s...
متن کامل2-Groups, 2-Characters, and Burnside Rings
We study 2-representations, i.e. actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended Burnside rings. Our main theorem is that the Ganter-Kapranov 2-character is a particular mark homomorphism of the Burnside ring. As an application we give a new proof of Osorno formula for the Ganter-Kapranov 2-charact...
متن کاملC 0-topology in Morse Theory
Let f be a Morse function on a closed manifold M , and v be a Riemannian gradient of f satisfying the transversality condition. The classical construction (due to Morse, Smale, Thom, Witten), based on the counting of flow lines joining critical points of the function f associates to these data the Morse complex M * (f, v). In the present paper we introduce a new class of vector fields (f-gradie...
متن کاملA ug 2 00 9 Robin Heat Semigroup and HWI Inequality on Manifolds with Boundary ∗
Let M be a complete connected Riemannian manifold with boundary ∂M , Q a bounded continuous function on ∂M , and L = ∆+Z for a C1-vector field Z on M . By using the reflecting diffusion process generated by L and its local time on the boundary, a probabilistic formula is presented for the semigroup generated by L on M with Robin boundary condition 〈N,∇f〉+ Qf = 0, where N is the inward unit norm...
متن کامل