Monotone Quotients of Surface Diffeomorphisms

Monotone Quotients of Surface Diffeomorphisms Andr

Variational Construction of Orbits of Twist Diffeomorphisms

In this paper, we construct certain random or chaotic orbits in certain exact area-preserving diffeomorphisms of the cylinder. The mappings we consider are finite compositions of monotone twist diffeomorphisms, all of the same sign (i.e., either all positive monotone or negative monotone). For simplicity, we consider only finite compositions of positive monotone twist diffeomorphisms, since the...

Gromov–Witten invariants of symplectic quotients and adiabatic limits

We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions to the symplectic vortex equations. Our main theorem asserts that the genus zero invariants of Hamiltonian group actions defined by these equations are related to the genus zero Gromov–Witten invariants of the symplectic quotient (in the monotone case) via a natural ring homomorphism from the equivariant ...

Dual closure operators and their applications

Departing from a suitable categorical description of closure operators, this paper dualizes this notion and introduces some basic properties of dual closure operators. Usually these operators act on quotients rather than subobjects, and much attention is being paid here to their key examples in algebra and topology, which include the formation of monotone quotients (Eilenberg-Whyburn) and conco...

L’hôpital’s Monotone Rule, Gromov’s Theorem, and Operations That Preserve the Monotonicity of Quotients

We study several operators T that when applied to both the numerator and denominator of an increasing, or decreasing, function u/v produce another increasing, or decreasing, function T (u)/T (v). We also give new proofs of the monotone form of L’Hôpital’s rule and of Gromov’s theorem.