Special Lagrangian submanifolds with isolated conical singularities. V.
Survey and applications

This is the last in a series of five papers math.DG/0211294, math.DG/0211295,
math.DG/0302355, math.DG/0302356 studying compact special Lagrangian
submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities
x_1,...,x_n locally modelled on special Lagrangian cones C_1,...,C_n in C^m
with isolated singularities at 0.
Readers are advised to begin with this paper. We survey the major results of
the previous four papers, giving brief explanations of the proofs. We apply the
results to describe the boundary of a moduli space of compact, nonsingular SL
m-folds N in M. We prove the existence of special Lagrangian connected sums N_1
# ... # N_k of SL m-folds N_1,...,N_k in M. We also study SL 3-folds with
T^2-cone singularities, proving results related to ideas of the author on
invariants of Calabi-Yau 3-folds and the SYZ Conjecture.
Let X be a compact SL m-fold with isolated conical singularities x_i and
cones C_i for i=1,...,n. The first paper math.DG/0211294 studied the regularity
of X near its singular points, and the the second paper math.DG/0211295 the
moduli space of deformations of X.
The third and fourth papers math.DG/0302355, math.DG/0302356 construct
desingularizations of X, realizing X as a limit of a family of compact,
nonsingular SL m-folds N^t in M for small t>0. Let L_i be an Asymptotically
Conical SL m-fold in C^m asymptotic to C_i at infinity. We make N^t by gluing
tL_i into X at x_i for i=1,...n.