$\mathrm{z}\mathrm{A}\mathrm{C}\mathrm{\Gamma }\mathrm{I}\mathrm{O}\mathrm{N}\mathrm{S}$ AND and and and and and and and and Ann. appear). appear). appear). Atiyah-SingerBrowder,

case coefficients compact compact Conference C. C.

DIFFEOMORPHISMS differentiable D.

$\mathrm{▹}\mathit{q}\mathit{u}\mathit{i}\mathit{v}\mathit{d}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathit{s}$ even

For function

group Groups groups groups groups,

have homeo- homotopy

in in invariant, $\mathit{i}\mathit{s}$

IERSEY J. $\mathrm{J}$,

Lie

mamfolds Math. morphisms, M.

$\mathrm{\prime }\mathrm{\prime }{\mathit{e}}^{\mathit{x}}\mathrm{1}\mathrm{/}\mathit{t}\mathrm{\ne }\mathrm{-}\mathrm{1}\mathrm{,}$ ${\mathit{L}}_{\mathit{t}}^{\mathrm{0}}\mathrm{(}{\mathit{Z}}_{\mathrm{2}}\mathrm{,}\mathrm{}\mathrm{(}\mathrm{-}\mathrm{1}{\mathrm{)}}^{\mathit{k}\mathrm{+}\mathrm{1}}\mathrm{)}\mathrm{\otimes }\mathit{Q}\mathrm{=}\mathrm{0}$

($\mathrm{(}\mathit{k}\mathrm{+}\mathrm{1}\mathrm{)}\mathit{i}\mathrm{\equiv }\mathrm{0}$ (4) $\mathit{q}\mathrm{\geqq }\mathrm{2}\mathit{k}\mathrm{+}\mathrm{1}{\mathit{Z}}_{\mathrm{2}}\mathrm{=}{\mathit{S}}^{\mathrm{0}}\mathrm{,}$ ${\mathit{B}}_{\mathit{k}\mathrm{.}\mathit{q}}\mathrm{=}\mathit{Q}$. ${\mathit{L}}_{\mathit{n}}\mathrm{(}\mathit{\pi }\mathrm{,}\mathrm{}\mathrm{1}\mathrm{)}\mathit{q}\mathrm{\equiv }\mathrm{-}\mathrm{1}\mathrm{\left(}\mathrm{4}\mathrm{\right)}$${\mathit{L}}_{\mathrm{4}\mathit{k}}^{\mathrm{0}}\mathrm{(}{\mathit{Z}}_{\mathrm{2}}\mathrm{,}\mathrm{}\mathrm{+}\mathrm{1}\mathrm{)}\mathrm{\otimes }\mathit{Q}\mathrm{,}$ ${\mathit{B}}_{\mathit{k}\mathrm{,}\mathit{q}}\mathrm{=}\mathrm{0}$

${\mathbb{R}}_{\mathrm{0}}^{\mathit{k}\mathrm{.}\mathit{q}}\mathrm{\otimes }\mathit{Q}\mathrm{\cong }{\mathit{B}}_{\mathit{k}\mathrm{.}\mathit{q}}\mathrm{+}{\mathit{L}}_{\mathit{k}\mathrm{+}\mathit{q}\mathrm{+}\mathrm{2}}^{\mathrm{0}}\mathrm{(}{\mathit{Z}}_{\mathrm{2}}\mathrm{,}\mathrm{}\mathrm{(}\mathrm{-}\mathrm{1}{\mathrm{)}}^{\mathit{k}\mathrm{+}\mathrm{1}}\mathrm{)}\mathrm{\otimes }\mathit{Q}$

NEW New Non-hnear notes) N.$\mathrm{3}\mathrm{f}$ of of on $\mathit{o}\mathit{n}$ Orleans,

28540 163 174-187. 1967. 1967) 1969. 1971] 1. 2. 3. 4. S. 6. 6. 92 field (1970), (mimeographed (New

$\mathrm{\setminus }\mathrm{\prime }\mathrm{t}\mathrm{o}$ (to (to -,

Petrie, PRINCETON Princeton PRINCETON, Princeton, Proc.REFERENCES representations Rothenberg

SEMIFREE smooth smoothing Sondow, Springer-Verlag, Sullivan, Surgery Surgery Surgery

$\mathrm{\Gamma }\mathit{h}\mathit{e}$ the the the the THEOREM theory T. T. Transformation fransformatim TriangulatingUNIVERSITY, University, unless unless

wall Wall, we where which with W.

York.