Difference between revisions of "Regularized moduli spaces"
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Finally, we need to check that for each pair <math>(b,b')\in\overline\mathcal{M}^0(x_0;\underline{x},y,\underline{x}'';\nu)\times\overline\mathcal{M}^0(y;\underline{x}';\nu)</math>, | Finally, we need to check that for each pair <math>(b,b')\in\overline\mathcal{M}^0(x_0;\underline{x},y,\underline{x}'';\nu)\times\overline\mathcal{M}^0(y;\underline{x}';\nu)</math>, | ||
| − | when considered as boundary point <math>(b,b')\in\partial \overline\mathcal{M}^1(x_0;x_1,\ldots,x_d;\nu)</math> has symplectic area <math>\omega((b,b')) = \omega(b) + \omega(b')</math> and weight function <math>\text{w}((b,b')) = (-1)^{\|\underline x\|} \text{w}(b) \text{w}(b')</math>. | + | when considered as boundary point <math>(b,b')\in\partial \overline\mathcal{M}^1(x_0;x_1,\ldots,x_d;\nu)</math>, has symplectic area <math>\omega((b,b')) = \omega(b) + \omega(b')</math> and weight function <math>\text{w}((b,b')) = (-1)^{\|\underline x\|} \text{w}(b) \text{w}(b')</math>. |
Revision as of 18:49, 26 May 2017
Given the moduli spaces of pseudoholomorphic polygons 
for each tuple of Lagrangians 
, generators 
, and a fixed compatible almost complex structure 
, we need to explain how to obtain regularizations 
for expected dimensions 
by a choice of perturbations 
.
Moreover, we need to choose these perturbations coherently to ensure that the boundary of each 1-dimensional part is given by Cartesian products of 0-dimensional parts,
TODO
Finally, we need to check that for each pair 
,
when considered as boundary point 
, has symplectic area 
and weight function 
.
