  Hamiltonians which are inaccessible in static systems can be engineered in
periodically driven many-body systems, i.e., Floquet many-body systems. We
propose to use interacting particles in a one-dimensional (1D) harmonic
potential with periodic kicking to investigate two-dimensional (2D) topological
and many-body physics. Depending on the driving parameters, the Floquet
Hamiltonian of single kicked harmonic oscillator has various lattice structures
in phase space. The noncommutative geometry of phase space gives rise to the
topology of the system. We investigate the effective interactions of particles
in phase space and find that the point-like contact interaction in quasi-1D
real space becomes a long-rang Coulomb-like interaction in phase space, while
the hardcore interaction in pure-1D real space becomes a confinement quark-like
potential in phase space. We also find that the Floquet exchange interaction
does not disappear even in the classical limit, and can be viewed as an
effective long-range spin-spin interaction induced by collision. Our proposal
may provide platforms to explore new physics and exotic phases by
\textit{Floquet many-body engineering}.
