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\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{>}}\relax \xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{ENTRY "1,3"}{\Row =1 \Col =3\relax \cfromid@ {1,3}\pfromc@ }% \xy@@ix@{{\entrybox }{I(V_{k-2}\otimes \sB )\ar [d] }}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {-}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@2,3\endcsname \ifx \next@ \relax \xyerror@RC {2,3}\else \next@ \fi }% \xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }% \xy@{PATHaction={\preconnect \dir {-}}}{}% \xy@@ix@{{\dir }{-}}\relax \xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{}}\relax \xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{>}}\relax \xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{ENTRY "2,1"}{\Row =2 \Col =1\relax \cfromid@ {2,1}\pfromc@ }% \xy@@ix@{{\entrybox }{}}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{ENTRY "2,2"}{\Row =2 \Col =2\relax \cfromid@ {2,2}\pfromc@ }% \xy@@ix@{{\entrybox }{V_{k-2}\otimes \sM \ar [r]^{\tilde {\delta }}\ar [d] }}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {-}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@2,3\endcsname \ifx \next@ \relax \xyerror@RC {2,3}\else \next@ \fi }% \xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }% \xy@{PATHaction={\preconnect \dir {-}}}{}% \xy@@ix@{{\dir }{-}}\relax \xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{}}\relax \xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{^}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@{}{\enter@ \DirectionfromtheDirection@ }% \xy@@ix@{\labelbox {\tilde {\delta }}}\relax \xy@{}{\setbox \z@ =\expandafter \object \the \toks 9 \advance \L@c \labelmargin@ \advance \R@c \labelmargin@ \advance \D@c \labelmargin@ \advance \U@c \labelmargin@ \setboxz@h {\kern \labelmargin@ \boxz@ \kern \labelmargin@ }\A@ =\X@c \B@ =\Y@c \belowDirection@ \xydashl@ \the \Edge@c \thr@@ \advance \A@ -\X@c \advance \B@ -\Y@c \advance \X@c 2\A@ \advance \Y@c 2\B@ \ht \z@ =\U@c \dp \z@ =\D@c \dimen@ =\L@c \advance \dimen@ \R@c \wd \z@ =\dimen@ \setbox \lastobjectbox@ =\hbox {\X@c =\L@c \Y@c =\z@ \Drop@@ }\drop@ {\box \lastobjectbox@ }{}\leave@ }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{>}}\relax \xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {-}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,2\endcsname \ifx \next@ \relax \xyerror@RC {3,2}\else \next@ \fi }% \xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }% \xy@{PATHaction={\preconnect \dir {-}}}{}% \xy@@ix@{{\dir }{-}}\relax \xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{}}\relax \xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{>}}\relax \xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{ENTRY "2,3"}{\Row =2 \Col =3\relax \cfromid@ {2,3}\pfromc@ }% \xy@@ix@{{\entrybox }{V_{k-2}\otimes \sB \ar [d] }}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {-}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[d]}{\def \thematrixCOORD@@ {[d]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,3\endcsname \ifx \next@ \relax \xyerror@RC {3,3}\else \next@ \fi }% \xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }% \xy@{PATHaction={\preconnect \dir {-}}}{}% \xy@@ix@{{\dir }{-}}\relax \xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{}}\relax \xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{>}}\relax \xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{ENTRY "3,1"}{\Row =3 \Col =1\relax \cfromid@ {3,1}\pfromc@ }% \xy@@ix@{{++}{\sS _k(N,\eps )}}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {-}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir ^{(}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,2\endcsname \ifx \next@ \relax \xyerror@RC {3,2}\else \next@ \fi }% \xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }% \xy@{PATHaction={\preconnect \dir {-}}}{}% \xy@@ix@{{\dir }{-}}\relax \xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir ^}{(}}\relax \xy@{\drop !Ch\dir ^{(}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{>}}\relax \xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{ENTRY "3,2"}{\Row =3 \Col =2\relax \cfromid@ {3,2}\pfromc@ }% \xy@@ix@{{\entrybox }{\protect \boldsymbol {\mathcal {M}}_k(N,\eps )\ar [r]^{\delta } }}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{\save }{\save@ }% \xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}% \xy@{~={\preconnect \dir {-}}}{}% \xy@{~/{}}{}% \xy@{~<{|<*h\dir {}}}{}% \xy@{~>{|>*h\dir {>}}}{}% \xy@{~+{}}{}% \xy@{}{\pfromc@ }% \xy@{[r]}{\def \thematrixCOORD@@ {[r]}}% \xy@{}{\expandafter \let \expandafter \next@ \csname Q@3,3\endcsname \ifx \next@ \relax \xyerror@RC {3,3}\else \next@ \fi }% \xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }% \xy@{PATHaction={\preconnect \dir {-}}}{}% \xy@@ix@{{\dir }{-}}\relax \xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{}}\relax \xy@{\drop !Ch\dir {}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{^}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@{}{\enter@ \DirectionfromtheDirection@ }% \xy@@ix@{\labelbox {\delta }}\relax \xy@{}{\setbox \z@ =\expandafter \object \the \toks 9 \advance \L@c \labelmargin@ \advance \R@c \labelmargin@ \advance \D@c \labelmargin@ \advance \U@c \labelmargin@ \setboxz@h {\kern \labelmargin@ \boxz@ \kern \labelmargin@ }\A@ =\X@c \B@ =\Y@c \belowDirection@ \xydashl@ \the \Edge@c \thr@@ \advance \A@ -\X@c \advance \B@ -\Y@c \advance \X@c 2\A@ \advance \Y@c 2\B@ \ht \z@ =\U@c \dp \z@ =\D@c \dimen@ =\L@c \advance \dimen@ \R@c \wd \z@ =\dimen@ \setbox \lastobjectbox@ =\hbox {\X@c =\L@c \Y@c =\z@ \Drop@@ }\drop@ {\box \lastobjectbox@ }{}\leave@ }% \xy@{|}{}% \xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }% \xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }% \xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }% \xy@{}{\leave@ }% \xy@@ix@{{!Ch\dir }{>}}\relax \xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }% \xy@{}{\Cbreak@@ }% \xy@{}{\Clast@@ }% \xy@{}{\setupDirection@ }% \xy@{PATHaction/{}}{}% \xy@{\restore }{\leave@ }% \xy@{ENTRY "3,3"}{\Row =3 \Col =3\relax \cfromid@ {3,3}\pfromc@ }% \xy@@ix@{{\entrybox }{\protect \boldsymbol {\mathcal {B}}_k(N,\eps )}}\relax \xy@{}{\expandafter \dropentry@ \the \toks 9}% \xy@{}{\leave@ }% \xy@{}{}% \xy@{\restore }{\leave@ }% \xy@{}{\edef \nextii@ {{\xy@minX@@ }{\xy@maxX@@ }{\xy@minY@@ }{\xy@maxY@@ }}\expandafter \xymatrix@insert@ \nextii@ }% \xy@{}{\leave@ }% \xyendcompiled