52 %Given a 0-blob diagram $x$ on $Y\times F$, we can choose a decomposition $K$ of $Y$ |
52 %Given a 0-blob diagram $x$ on $Y\times F$, we can choose a decomposition $K$ of $Y$ |
53 %such that $x$ is splittable with respect to $K\times F$. |
53 %such that $x$ is splittable with respect to $K\times F$. |
54 %This defines a filtration degree 0 element of $\bc_*^\cF(Y)$ |
54 %This defines a filtration degree 0 element of $\bc_*^\cF(Y)$ |
55 |
55 |
56 We will define $\phi$ using a variant of the method of acyclic models. |
56 We will define $\phi$ using a variant of the method of acyclic models. |
57 Let $a\in S_m$ be a blob diagram on $Y\times F$. |
57 Let $a\in \cS_m$ be a blob diagram on $Y\times F$. |
58 For $m$ sufficiently small there exist decompositions of $K$ of $Y$ into $k$-balls such that the |
58 For $m$ sufficiently small there exists a decomposition $K$ of $Y$ into $k$-balls such that the |
59 codimension 1 cells of $K\times F$ miss the blobs of $a$, and more generally such that $a$ is splittable along $K\times F$. |
59 codimension 1 cells of $K\times F$ miss the blobs of $a$, and more generally such that $a$ is splittable along $K\times F$. |
60 Let $D(a)$ denote the subcomplex of $\bc_*^\cF(Y)$ generated by all $(a, \bar{K})$ |
60 Let $D(a)$ denote the subcomplex of $\bc_*^\cF(Y)$ generated by all $(a, \bar{K})$ |
61 such that each $K_i$ has the aforementioned splittable property |
61 such that each $K_i$ has the aforementioned splittable property |
62 (see Subsection \ref{ss:ncat_fields}). |
62 (see Subsection \ref{ss:ncat_fields}). |
63 \nn{need to define $D(a)$ more clearly; also includes $(b_j, \bar{K})$ where |
63 \nn{need to define $D(a)$ more clearly; also includes $(b_j, \bar{K})$ where |