202 For these reasons and others, it is desirable to |
202 For these reasons and others, it is desirable to |
203 extend to above framework to incorporate ideas from derived categories. |
203 extend to above framework to incorporate ideas from derived categories. |
204 |
204 |
205 One approach to such a generalization might be to simply define a |
205 One approach to such a generalization might be to simply define a |
206 TQFT via its gluing formulas, replacing tensor products with |
206 TQFT via its gluing formulas, replacing tensor products with |
207 derived tensor products. |
207 derived tensor products (c.f. \cite{1011.1958}). |
208 \nn{maybe cite Kh's paper on links in $S^1\times S^2$} |
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209 However, it is probably difficult to prove |
208 However, it is probably difficult to prove |
210 the invariance of such a definition, as the object associated to a manifold |
209 the invariance of such a definition, as the object associated to a manifold |
211 will a priori depend on the explicit presentation used to apply the gluing formulas. |
210 will a priori depend on the explicit presentation used to apply the gluing formulas. |
212 We instead give a manifestly invariant construction, and |
211 We instead give a manifestly invariant construction, and |
213 deduce from it the gluing formulas based on $A_\infty$ tensor products. |
212 deduce from it the gluing formulas based on $A_\infty$ tensor products. |