Let T × M → M be a Hamiltonian torus action on a connected symplectic manifold M for which the associated moment map Φ : M → t∗ is proper as a map into a convex open set ρ ⊆ t∗. We consider a closed submanifold Q of M and show that under certain local conditions on Q one has Φ(Q) = Φ(M). We apply this result in the special case that Q arises as the fixed point set of some involution σ on M whic...

We develop a theory of Spanier–Whitehead duality in categories with cofibrations and weak equivalences (Waldhausen categories, for short). This includes L–theory, the involution on K–theory introduced by [Vo] in a special case, and a map Ξ relating L–theory to the Tate spectrum of Z/2 acting on K–theory. The map Ξ is a distillation of the long exact Rothenberg sequences [Sha], [Ra1], [Ra2], inc...

The Banach Poisson geometry of multi-diagonal Hamiltonian systems having infinitely many integrals in involution is studied. It is shown that these systems can be considered as generalizing the semi-infinite Toda lattice which is an example of a bidiagonal system, a case to which special attention is given. The generic coadjoint orbits of the Banach Lie group of bidiagonal bounded operators are...

The Banach Poisson geometry of multi-diagonal Hamiltonian systems having infinitely many integrals in involution is studied. It is shown that these systems can be considered as generalizing the semi-infinite Toda lattice which is an example of a bidiagonal system, a case to which special attention is given. The generic coadjoint orbits of the Banach Lie group of bidiagonal bounded operators are...

In the paper, we study real forms of complex generic Neumann system. We prove that are completely integrable Hamiltonian systems. The system is an example more general Mumford characterized by Lax pair (Lℂ(λ), Mℂ(λ)) 2 × matrices, where and Uℂ(λ), Vℂ(λ), Wℂ(λ) suitable polynomials. topology a regular level set moment map form determined positions roots with respect to position values parameters...

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

Let G be a complex semisimple Lie group and τ a complex an-tilinear involution that commutes with the Cartan involution. If H denotes the connected subgroup of τ-fixed points in G, and K is maximally compact, each H-orbit in G/K can be equipped with a Poisson structure as described by Evens and Lu. We consider symplectic leaves of certain such H-orbits and show that an application of the symple...

Let S be a Todorov surface, i.e., a minimal smooth surface of general type with q = 0 and pg = 1 having an involution i such that S/i is birational to a K3 surface and such that the bicanonical map of S is composed with i. The main result of this paper is that, if P is the minimal smooth model of S/i, then P is the minimal desingularization of a double cover of P ramified over two cubics. Furth...

Let (g, k) be a reductive symmetric superpair of even type, i.e. so that there exists an even Cartan subspace a ⊂ p. The restriction map S(p) → S(a) where W = W (g0 : a) is the Weyl group, is injective. We determine its image explicitly. In particular, our theorem applies to the case of a symmetric superpair of group type, i.e. (k ⊕ k, k) with the flip involution where k is a classical Lie supe...

The purpose of this note is to give a simple description of a complete family of functions in involution on certain hermitian symmetric spaces. This family obtained via bi-hamiltonian approach using the Bruhat Poisson structure is especially simple for projective spaces, where the formulas in terms of the moment map coordinates are presented. Relations with the Toda lattice are outlined (we pla...