We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the eleven dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on MorrisonNikulin involutions, these are Nikulin involutions wh...

Let In be the class of all signed involutions in the hyperoctahedral group Bn and let In(T ) be the set of involutions in In which avoid a set T of signed patterns. In this paper, we complete a further case of the program initiated by Simion and Schmidt [6] by enumerating In(T ) for all signed permutations T ⊆ B2.

As a first step to a detailed study of orientifolds of Gepner models associated with CalabiYau manifolds, we construct crosscap states associated with anti-holomorphic involutions (with fixed points) of Calabi-Yau manifolds. We argue that these orientifolds are dual to M-theory compactifications on (singular) seven-manifolds with G2 holonomy. Using the spacetime picture as well as the M-theory ...

We incorporate pearly Floer trajectories into the transversality scheme for pseudoholomorphic maps introduced by Cieliebak-Mohnke [12] and further developed by Ionel-Parker [33], Wendl [59], and Gerstenberger [29]. By choosing generic domain-dependent almost complex structures we obtain zero and onedimensional moduli spaces with the structure of cell complexes with rational fundamental classes....

We consider in this work the enumeration of involutions by descent sets, and based on that, by descent numbers. Formulas of the number of involutions with a prescribed descent set, with a prescribed descent number and Frobenius-type formulas are given.

In this paper, we study the essential dimension of classes of central simple algebras with involutions of index less or equal to 4. Using structural theorems for simple algebras with involutions, we obtain the essential dimension of projective and symplectic groups of small degree.

We show that there are exactly nine distinct PL involutions on the nonorientable 2-sphere bundle over Sl, up to PL equivalences. This, together with results of [1], [3] and [8], classifies all PL involutions on the 2sphere bundles over S1.

Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces real forms of complex algebras, are well-studied in the context symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, introduce concept pseudo-involution, an automorphism which is only required act involutively on stable Cartan subalgebra, pseudo-fixed-point natural substitute fo...

In this paper we give a simple characterization of the isomorphy classes of involutions of SL(2, k) with k any field of characteristic not 2. We also classify the isomorphy classes of involutions for k algebraically closed, the real numbers, the -adic numbers and finite fields. We determine in which cases the corresponding fixed point group H is k-anisotropic. In those cases the corresponding s...

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...