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zZHFexfdmMAd_CXU#M>Mc3$!NcOT9SEsx;hVgKNC$)aU|S;@0ivD@YKQgZFG#56w9z ze=j0jEVxztR;f5HIQ-9xxXlEXWrhll6A0qrO6R3#q4=-UHhp>)OBj4Reh*hw1%6*% z8Geu|ki#0J=Aomi);7n)f&qoVDF6fs{P8+uX5s$77j3jGEUZxYy!@1$|Jf*=(UAWf z0Q>+Reh{$Dnw6y!TA1g5m+^r>T>QNM+s4ny&Ck#Ew++O@&6RGW+qnM7;2#?R^bfOKK(7DlMDYI$3c$_H^*2KR9xm>`8~Mlf50d~MZvKCO z`GCBCDTN;Z1n~YZGQj_l7VwWO{*D?5UKfr%t{->Mxc)0&NXx{(P6M&Bw_^&fR|3CDD v{s<&}U5v#N`2Qc=!oo~O$RZ-h?jB}t9zJeX*2sS-25|$qkm=~8Rb>7TOgXCt diff --git a/src/main.typ b/src/main.typ index 3b7ff39..b33f027 100644 --- a/src/main.typ +++ b/src/main.typ @@ -1277,7 +1277,7 @@ Possiamo ora mostrare l'invarianza per scelta di punto base di $Omega_K (p)$. ) } - - Se $i$ è un sotto-incrocio in $K(p)$ allora $i$ sarà il primo incrocio nella sequenza di scambi ed avremo $i = n$. La situazione sarà quindi la seguente: + - Se $i$ è un sotto-incrocio in $K(p)$, allora $i$ sarà il primo incrocio nella sequenza di scambi ed avremo $i = n$. La situazione sarà quindi la seguente: #{ set align(center) @@ -1476,7 +1476,7 @@ A questo punto possiamo vedere che $L_K$ verifica gli assiomi della @kauffman-po Come ultimo risultato vediamo che $L_K$ è un invariante di isotopia regolare. #lemma[ - Siano $K, K'$ diagrammi di link equivalenti a meno di isotopia regolare allora $L_K (a, z) = L_(K') (a, z)$. + Siano $K, K'$ diagrammi di link equivalenti a meno di isotopia regolare, allora $L_K (a, z) = L_(K') (a, z)$. ] #proof[ @@ -1484,13 +1484,13 @@ Come ultimo risultato vediamo che $L_K$ è un invariante di isotopia regolare. - Mossa II: Ci sono vari casi in base a se la mossa II riguarda una o più componenti: - - Se la mossa è su una sola componente allora ci basta scegliere il punto base come segue + - Se la mossa è su una sola componente, allora ci basta scegliere il punto base come segue #figure(image("assets/move-2-base-points.jpg", width: 6cm)) in questo modo i due incroci non compariranno nella sequenza di scambi. Tutti i termini di @kauffman-rec-single-component saranno invarianti per mosse di tipo II e lo sarà anche $L_K$. - - Se la mossa riguarda più componenti allora il caso peggiore è il seguente + - Se la mossa riguarda più componenti, allora il caso peggiore è il seguente #figure(image("assets/move-2-base-points-bad.png", width: 3cm)) @@ -1572,7 +1572,7 @@ Come ultimo risultato vediamo che $L_K$ è un invariante di isotopia regolare. - Mossa III: - - Se la mossa è su fili di una sola componente allora possiamo scegliere il punto base in modo che sia sul filo che passa sopra tra i tre, e saremo nella situazione seguente: + - Se la mossa è su fili di una sola componente, allora possiamo scegliere il punto base in modo che sia sul filo che passa sopra tra i tre, e saremo nella situazione seguente: $ #image("assets/derived/atlas-move-3-0.png", height: 2.25cm)