equal
deleted
inserted
replaced
57 In other words $\bd : \bc_1(X) \to \bc_0(X)$ is given by |
57 In other words $\bd : \bc_1(X) \to \bc_0(X)$ is given by |
58 just erasing the blob from the picture |
58 just erasing the blob from the picture |
59 (but keeping the blob label $u$). |
59 (but keeping the blob label $u$). |
60 |
60 |
61 Note that the skein space $A(X)$ |
61 Note that the skein space $A(X)$ |
62 is naturally isomorphic to $\bc_0(X)/\bd(\bc_1(X))) = H_0(\bc_*(X))$. |
62 is naturally isomorphic to $\bc_0(X)/\bd(\bc_1(X))) = H_0(\bc_*(X))$. This is Property \ref{property:skein-modules}, and also used in the second half of Property \ref{property:contractibility}. |
63 |
63 |
64 $\bc_2(X)$ is, roughly, the space of all relations (redundancies, syzygies) among the |
64 $\bc_2(X)$ is, roughly, the space of all relations (redundancies, syzygies) among the |
65 local relations encoded in $\bc_1(X)$. |
65 local relations encoded in $\bc_1(X)$. |
66 More specifically, $\bc_2(X)$ is the space of all finite linear combinations of |
66 More specifically, $\bc_2(X)$ is the space of all finite linear combinations of |
67 2-blob diagrams, of which there are two types, disjoint and nested. |
67 2-blob diagrams, of which there are two types, disjoint and nested. |