Fukayayegwyw.tn stopsLet A be a conical subset of T*M
,that is
one preserved by the scalar action on fibres .
Then the above theorems raise the
question : what is the image of the
equivalence shown under the givenrestriction ?
DC2Con(M)) t DFukwTT*M)
U U
DC2Con IM)) Is ?
To answer this , we define the category" with stops
"DfukYT ,
with objects givenby Lagrangian which avoid A inthe
limit 131→ a for Cm ,3) ET *M.
Using this , we have the following recentresult of Ganatra-Pardon-Shende COPS] :
Thm DCQCon IM)) t DFukwTT*M)
- x
Trimm .
Combining the work of Kawasaki and
GPS , we obtain the following statementof homological MS :
DCKohlXs)) (B-model)
DCQCon xdTt ))
→ DFukwTT* IT) (A -model)Xs
Rey In fact , this work extends to toric
stacks,in sense of
,for instance ,
Geraschenko -Satriani [GS] .
Note for 3-fold example we can take
a resolution of Gay -zw = O) C 04.
See Donovan-Kawasaki CDW] ,section 4
.
2.
fwthertop
See [T2] for correspondence between
Dehn twist operations on symplectic manifoldsand symmetries of DRCoh (XD under
mirror symmetry .