We show that for compact Riemannian manifolds of dimension at least 3 with nonempty boundary, we can modify the manifold by performing surgeries codimension 2 or higher, while keeping Steklov spectrum nearly unchanged. This shows certain changes in topology a domain do not have an effect when considering shape optimization questions eigenvalues dimensions and higher. Our result generalizes 1-di...

Let A = {x1, . . . , xn} be a subspace arrangement with a geometric lattice such that codim(x) ≥ 2 for every x ∈ A. Using rational homotopy theory, we prove that the complement M(A) is rationally elliptic if and only if the sum x 1 + . . . + x n is a direct sum. The homotopy type of M(A) is also given : it is a product of odd dimensional spheres. Finally, some other equivalent conditions are gi...

We prove an embedding theorem for maps from a finite complex into a Poincaré duality space. The proof uses fiberwise homotopy theory.

We give an off-shell formulation of N = 2 Poincaré supergravity in five dimensions. e-mail: [email protected]

The operad Lie can be constructed as the operad of primitives PrimAs from the operad As of associative algebras. This is reflected by the theorems of Friedrichs, Poincaré-Birkhoff-Witt and Cartier-Milnor-Moore. We replace the operad As by families of free operads P, which include the operad Mag freely generated by a noncommutative non-associative binary operation and the operad of Stasheff poly...