We classify, in terms of simple algebraic equations, the fixed point sets of the moduli space of stable bundles over genus 2 curves with anti-holomorphic involutions. 1991 MS Classification: 14H60, 51M30.

In this note we prove that the space of linear anti-symplectic involutions is the homogenous space Gl(n,R)\Sp(n). This result is motivated by the study of symmetric periodic orbits in the restricted 3-body problem.

This is an expanded version of the talk given by first author at conference “Topology, Geometry, and Dynamics: Rokhlin – 100”. The purpose this was to explain our current results on classification rational symplectic 4-manifolds equipped with anti-symplectic involution. A detailed exposition will appear elsewhere.

Building on previous results [17, 35], we complete the classification of compact oriented Einstein 4-manifolds with $$\det (W^+) > 0$$ . There are, up to diffeomorphism, exactly 15 manifolds that carry such metrics, and, each these manifolds, metrics sweep out one connected component corresponding moduli space.

Let Σg,b denote a closed orientable surface of genus g with b punctures and let Mod(Σg,b) denote its mapping class group. In [Luo] Luo proved that if the genus is at least 3, Mod(Σg,b) is generated by involutions. He also asked if there exists a universal upper bound, independent of genus and the number of punctures, for the number of torsion elements/involutions needed to generate Mod(Σg,b). B...

We describe four types of inner involutions of the Cartan-Weyl basis providing (for |q| = 1 and q real) three types of real quantum Lie algebras: Uq(O(3, 2)) (quantum D = 4 anti-de-Sitter), Uq(O(4, 1)) (quantum D = 4 de-Sitter) and Uq(O(5)). We give also two types of inner involutions of the Cartan-Chevalley basis of Uq(Sp(4;C)) which can not be extended to inner involutions of the Cartan-Weyl ...

In this paper, confirming a conjecture of Kaplan et al., we prove that every abelian group G, which is of odd order or contains exactly three involutions, has the zerosum-partition property. As a corollary, every tree with |G| vertices and at most one vertex of degree 2 is G-anti-magic.