text/blobdef.tex
changeset 332 160ca7078ae9
parent 321 76c301fdf0a2
child 342 1d76e832d32f
equal deleted inserted replaced
329:eb03c4a92f98 332:160ca7078ae9
   178     \bd(b) = \sum_{j=1}^{k} (-1)^{j+1} E_j(b).
   178     \bd(b) = \sum_{j=1}^{k} (-1)^{j+1} E_j(b).
   179 }
   179 }
   180 The $(-1)^{j+1}$ factors imply that the terms of $\bd^2(b)$ all cancel.
   180 The $(-1)^{j+1}$ factors imply that the terms of $\bd^2(b)$ all cancel.
   181 Thus we have a chain complex.
   181 Thus we have a chain complex.
   182 
   182 
       
   183 Note that Property \ref{property:functoriality}, that the blob complex is functorial with respect to homeomorphisms, is immediately obvious from the definition. A homeomorphism acts in an obvious on blobs and on fields.
       
   184 
   183 We define the {\it support} of a blob diagram $b$, $\supp(b) \sub X$, 
   185 We define the {\it support} of a blob diagram $b$, $\supp(b) \sub X$, 
   184 to be the union of the blobs of $b$.
   186 to be the union of the blobs of $b$.
   185 For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram),
   187 For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram),
   186 we define $\supp(y) \deq \bigcup_i \supp(b_i)$.
   188 we define $\supp(y) \deq \bigcup_i \supp(b_i)$.
   187 
   189