equal
deleted
inserted
replaced
1136 \begin{equation*} |
1136 \begin{equation*} |
1137 \hom_A(\bc_*(M), \bc_*(N)) \ot \bc_*(M) \ot_A \bc_*(R) \to \bc_*(N) \ot_A \bc_*(R) . |
1137 \hom_A(\bc_*(M), \bc_*(N)) \ot \bc_*(M) \ot_A \bc_*(R) \to \bc_*(N) \ot_A \bc_*(R) . |
1138 \end{equation*} |
1138 \end{equation*} |
1139 We think of this map as being associated to a surgery which cuts $M$ out of $M\cup_E R$ and |
1139 We think of this map as being associated to a surgery which cuts $M$ out of $M\cup_E R$ and |
1140 replaces it with $N$, yielding $N\cup_E R$. |
1140 replaces it with $N$, yielding $N\cup_E R$. |
1141 (This is a more general notion of surgery that usual: $M$ and $N$ can be any manifolds |
1141 (This is a more general notion of surgery than usual: $M$ and $N$ can be any manifolds |
1142 which share a common boundary.) |
1142 which share a common boundary.) |
1143 In analogy to Hochschild cochains, we will call elements of $\hom_A(\bc_*(M), \bc_*(N))$ ``blob cochains". |
1143 In analogy to Hochschild cochains, we will call elements of $\hom_A(\bc_*(M), \bc_*(N))$ ``blob cochains". |
1144 |
1144 |
1145 Recall (Theorem \ref{thm:evaluation}) that chains on the space of mapping cylinders also act on the |
1145 Recall (Theorem \ref{thm:evaluation}) that chains on the space of mapping cylinders also act on the |
1146 blob complex. |
1146 blob complex. |