Higher algebraic structures in Hamiltonian Floer theory

Monodromy in Hamiltonian Floer Theory

Schwarz showed that when a closed symplectic manifold (M,ω) is symplectically aspherical (i.e. the symplectic form and the first Chern class vanish on π2(M)) then the spectral invariants, which are initially defined on the universal cover of the Hamiltonian group, descend to the Hamiltonian group Ham(M,ω). In this note we describe less stringent conditions on the Chern class and quantum homolog...

Algebraic structures in automata and databases theory

Inevitably, reading is one of the requirements to be undergone. To improve the performance and quality, someone needs to have something new every day. It will suggest you to have more inspirations, then. However, the needs of inspirations will make you searching for some sources. Even from the other people experience, internet, and many books. Books and internet are the recommended media to hel...

Hamiltonian handleslides for Heegaard Floer homology

A g-tuple of disjoint, linearly independent circles in a Riemann surface Σ of genus g determines a ‘Heegaard torus’ in its g-fold symmetric product. Changing the circles by a handleslide produces a new torus. It is proved that, for symplectic forms with certain properties, these two tori are Hamiltonian-isotopic Lagrangian submanifolds. This provides a new route to the handleslide-invarianceof ...

Alternative Algebraic Structures from Bi-hamiltonian Quantum Systems

We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg picture in terms of deformations of the associative product on the space of observables.

Algebraic aspects of higher nonabelian Hodge theory