\( \def\CC{{\mathbb C}} \def\RR{{\mathbb R}} \def\NN{{\mathbb N}} \def\ZZ{{\mathbb Z}} \def\TT{{\mathbb T}} \def\CF{{\operatorname{CF}^\bullet}} \def\HF{{\operatorname{HF}^\bullet}} \def\SH{{\operatorname{SH}^\bullet}} \def\ot{{\leftarrow}} \def\st{\;:\;} \def\Fuk{{\operatorname{Fuk}}} \def\emprod{m} \def\cone{\operatorname{Cone}} \def\Flux{\operatorname{Flux}} \def\li{i} \def\ev{\operatorname{ev}} \def\id{\operatorname{id}} \def\grad{\operatorname{grad}} \def\ind{\operatorname{ind}} \def\weight{\operatorname{wt}} \def\Sym{\operatorname{Sym}} \def\HeF{\widehat{CHF}^\bullet} \def\HHeF{\widehat{HHF}^\bullet} \def\Spinc{\operatorname{Spin}^c} \def\min{\operatorname{min}} \def\div{\operatorname{div}} \def\SH{{\operatorname{SH}^\bullet}} \def\CF{{\operatorname{CF}^\bullet}} \def\Tw{{\operatorname{Tw}}} \def\Log{{\operatorname{Log}}} \def\TropB{{\operatorname{TropB}}} \def\wt{{\operatorname{wt}}} \def\Span{{\operatorname{span}}} \def\Crit{\operatorname{Crit}} \def\CritVal{\operatorname{CritVal}} \def\FS{\operatorname{FS}} \def\Sing{\operatorname{Sing}} \def\Coh{\operatorname{Coh}} \def\Vect{\operatorname{Vect}} \def\into{\hookrightarrow} \def\tensor{\otimes} \def\CP{\mathbb{CP}} \def\eps{\varepsilon} \) SympSnip:

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definition 0.0.1 [Arn80]

Let \(\{L_0, \ldots, L_k\}\) be Lagrangian submanifolds of \(X\). A Lagrangian cobordism with positive ends \(L_0, \ldots L_k\) is a Lagrangian submanifold \(K\subset X\times T^*\RR\) for which there exists a compact subset \(D\subset \CC\) so that : \[K\setminus( \pi_\CC^{-1}(D))=\bigcup_{i=0}^k L_i\times \ell_i.\] Here, the \(\ell_i\) are rays of the form \(\ell_i(t)=i\cdot \jmath +t\), where \(t\in \RR_{\geq 0}\). We denote such a cobordism \(K:(L_0,L_1, \ldots L_k)\rightsquigarrow \emptyset\).

References

[Arn80]Vladimir Igorevich Arnol'd. Lagrange and Legendre cobordisms. i. Funktsional'nyi Analiz i ego Prilozheniya, 14(3):1--13, 1980.