Reidemeister Torsion in Floer--Novikov Theory and Counting pseudo-holomorphic tori, II

Abstract

This is the second part of an article in two parts, which builds the foundation of a Floer-theoretic invariant, \(I_{\rm F}\). (See [Y-J. Lee, Reidemeister torsion in Floer--Novikov theory and counting pseudo-holomorphic tori, I, J. Symplectic Geom. >3 (2005), no. 2, 221--311.] for Part I). Having constructed \(I_{\rm F}\) and outlined a proof of its invariance based on bifurcation analysis in Part I, in this part we prove a series of gluing theorems to confirm the bifurcation behavior predicted in Part I. These gluing theorems are different from (and much harder than) the more conventional versions in that they deal with broken trajectories or broken orbits connected at degenerate rest points which are not Morse--Bott. The issues of orientation and signs are also settled in the last section. This part is strongly >dependent on Part I, and is meant only for readers familiar with the previous part of this article.