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For each representative $\mathfrak{B}$ of a bordism class in the free loopspace of a manifold, we associate a moduli space of finite length Floercylinders in the cotangent bundle. The left end of the Floer cylinder isrequired to be a lift of one of the loops in $\mathfrak{B}$, and the right endis required to lie on the zero section. Under certain assumptions on theHamiltonian functions, the length of the Floer cylinder is a smooth properfunction, and evaluating the level sets at the right end produces a family ofloops cobordant to $\mathfrak{B}$. The argument produces arbitrarily long Floercylinders with certain properties. We apply this to prove an existence resultfor 1-periodic orbits of certain Hamiltonian systems in cotangent bundles, andalso to estimate the relative Gromov width of starshaped domains in certaincotangent bundles. The moduli space is similar to moduli spaces considered byAbbondandolo-Schwarz and Abouzaid for Tonelli Hamiltonians. The Hamiltonians weconsider are not Tonelli, but rather of ``contact-type'' in the symplectizationend.

Bordism classes of loops and Floer's equation in cotangent bundles