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44 |
44 |
45 Let $f: P \times X \to X$ be a family of homeomorphisms (e.g. a generator of $CH_*(X)$) |
45 Let $f: P \times X \to X$ be a family of homeomorphisms (e.g. a generator of $CH_*(X)$) |
46 and let $S \sub X$. |
46 and let $S \sub X$. |
47 We say that {\it $f$ is supported on $S$} if $f(p, x) = f(q, x)$ for all |
47 We say that {\it $f$ is supported on $S$} if $f(p, x) = f(q, x)$ for all |
48 $x \notin S$ and $p, q \in P$. Equivalently, $f$ is supported on $S$ if |
48 $x \notin S$ and $p, q \in P$. Equivalently, $f$ is supported on $S$ if |
49 there is a family of homeomorphisms $f' : P \times S \to S$ and a `background' |
49 there is a family of homeomorphisms $f' : P \times S \to S$ and a ``background" |
50 homeomorphism $f_0 : X \to X$ so that |
50 homeomorphism $f_0 : X \to X$ so that |
51 \begin{align*} |
51 \begin{align*} |
52 f(p,s) & = f_0(f'(p,s)) \;\;\;\; \mbox{for}\; (p, s) \in P\times S \\ |
52 f(p,s) & = f_0(f'(p,s)) \;\;\;\; \mbox{for}\; (p, s) \in P\times S \\ |
53 \intertext{and} |
53 \intertext{and} |
54 f(p,x) & = f_0(x) \;\;\;\; \mbox{for}\; (p, x) \in {P \times (X \setmin S)}. |
54 f(p,x) & = f_0(x) \;\;\;\; \mbox{for}\; (p, x) \in {P \times (X \setmin S)}. |