pnas/pnas.tex
changeset 714 e541b222dceb
parent 712 e982f12f163b
child 735 bd0d5b2155a7
equal deleted inserted replaced
713:eafdb7806df3 714:e541b222dceb
  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.