arXiv subjects
Publications and source records attributed to Joel Robbin.
We define combinatorial Floer homology of a transverse pair of noncontractibe nonisotopic embedded loops in an oriented 2-manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology.
The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy decompositions and Fredholm intersection theory in the loop space of the target manifold.
We prove a formula that expresses the Viterbo-Maslov index of a smooth strip in an oriented 2-manifold with boundary curves contained in 1-dimensional submanifolds in terms the degree function on the complement of the union of the two submanifolds.