Author Description

The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented img style="width:8px;height:12px;margin-right:0.053em" src="http://cdn.mathjax.org/mathjax/2.3-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png" -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a img style="width:8px;height:12px;margin-right:0.053em" src="http://cdn.mathjax.org/mathjax/2.3-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png" -manifold.