<math>{\mathbb K}=\Q</math> or <math>{\mathbb K}=\Z_2</math>, with a variable <math>T</math>,
 
<math>{\mathbb K}=\Q</math> or <math>{\mathbb K}=\Z_2</math>, with a variable <math>T</math>,
 
<center>
 
<center>
<math>\Lambda := \Lambda_{\mathbb K} := \left\{ \sum_{i=0}^\infty a_i T^{\lambda_i} \,\left|\, \R\ni \lambda_i \underset {i\to\infty}{\to} \infty , a_i\in \mathbb{K} \right.\right\}</math>
+
<math>\textstyle
 +
\Lambda := \Lambda_{\mathbb K} := \left\{ \sum_{i=0}^\infty a_i T^{\lambda_i} \,\left|\, \R\ni \lambda_i \underset {i\to\infty}{\to} \infty , a_i\in \mathbb{K} \right.\right\}</math>
 
</center>
 
</center>
    
Now for two Lagrangians <math>L_0, L_1 \subset M</math> that are transverse (i.e. <math> T_x L_0 \oplus T_x L_1 = T_x M \;\text{for each}\; x\in L_0\cap L_1</math>) and hence have a finite set of intersection points, the natural choice of morphism space is the Floer chain complex
 
Now for two Lagrangians <math>L_0, L_1 \subset M</math> that are transverse (i.e. <math> T_x L_0 \oplus T_x L_1 = T_x M \;\text{for each}\; x\in L_0\cap L_1</math>) and hence have a finite set of intersection points, the natural choice of morphism space is the Floer chain complex
 
<center>
 
<center>
<math>\text{Hom}(L_0,L_1) := \sum_{x\in L_0\cap L_1} \Lambda \, x </math>.
+
<math>\textstyle
 +
\text{Hom}(L_0,L_1) := \sum_{x\in L_0\cap L_1} \Lambda \, x </math>.
 
</center>
 
</center>
       
When considering the isomorphism space <math>\text{Hom}(L,L)</math> of a fixed Lagrangian <math>L_0 = L_1=L</math>, then the Hamiltonian symplectomorphism <math>\phi</math> can be obtained by lifting a Morse function <math>f: L \to \R</math> to a Hamiltonian function in a Lagrangian neighborhood <math> T^*L \subset M</math>. After extending it suitably, the intersection points can be identified with the critical points, <math>\phi(L)\cap L = \text{Crit} f</math>. Thus in this case we define the morphism space by the Morse chain complex
 
When considering the isomorphism space <math>\text{Hom}(L,L)</math> of a fixed Lagrangian <math>L_0 = L_1=L</math>, then the Hamiltonian symplectomorphism <math>\phi</math> can be obtained by lifting a Morse function <math>f: L \to \R</math> to a Hamiltonian function in a Lagrangian neighborhood <math> T^*L \subset M</math>. After extending it suitably, the intersection points can be identified with the critical points, <math>\phi(L)\cap L = \text{Crit} f</math>. Thus in this case we define the morphism space by the Morse chain complex
<center><math>\text{Hom}(L,L) :=  \sum_{x\in \text{Crit} f} \Lambda \, x </math>.</center>
+
<center><math>\textstyle
 +
\text{Hom}(L,L) :=  \sum_{x\in \text{Crit} f} \Lambda \, x </math>.</center>
    
Each of the morphism spaces is a vector space over the Novikov field <math>\Lambda=\Lambda_{\mathbb K}</math>.
 
Each of the morphism spaces is a vector space over the Novikov field <math>\Lambda=\Lambda_{\mathbb K}</math>.
 
To simplify notation, we will in the following use the universal construction of these vector spaces as
 
To simplify notation, we will in the following use the universal construction of these vector spaces as
 
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<center>