Algebraic Topology Göttingen 1984: Proceedings of a by C. Allday, V. Puppe (auth.), Larry Smith (eds.)

By C. Allday, V. Puppe (auth.), Larry Smith (eds.)

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Additional info for Algebraic Topology Göttingen 1984: Proceedings of a Conference held in Göttingen, Nov. 9–15, 1984

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Then F(i) = t. eo if there exist F' = (F N F') ~ { t ' } , t,t' C T I s' < t'} and {s C F I s > t} = {s' C F' I s' > t'}o If to be k - w a l l - n e i g h b o u r s we denote this by with t # t' and F = in w h i c h case we have n e c e s s a r i l y I s < t} = {s' C F' F' and starting with {s e F and if T is locally finite-dimensional, we define t = F(k) or - equivalently - t' = F'(k) Pure and locally pure tessellations: We define a t e s s e l l a t i o n and if all flags in F(T) T to be pure if have the same cardinality.

Xi J denoting , respectively study × (-I),(14)(35) the c o s e ~ with × (-l)> and "A "~l -< A "Bj ~ i _< j and of the 2-sphere. the concept set° It turns out that the former and dualization and to the subgroups decomposition and observations gives To,T I , A 1 =: <(13)(45) the dodecahedral j C JI "(a I ..... an) j (b I ..... bn)" a i m 0(2) with respect A o=: <(14)(32) for to the "tile" t(a I ..... an ) =: {(x I ..... x n) E ~ n a i m I(2)}; 2 (a i - bi)(b i - I) m 0(2) (a I .... ,an) J (ai+l)/2 if aj= j E Jo' (the construction of the topological real- one behaves much nicer with of the "star-complex") than the latter.

A short ~ A C and D are free abelian. C~C homology. 3). 2). We show t h a t F 4 depends For the c o m p u t a t i o n of the c l a s s i f y i n g z4 which p o s s i b l y b 4 6 H o m ( H 4 , r H 2) and on the e x t e n s i o n carry a b e l i a n functor respectively. X') In §3 b e l o w we compute (b 4, the image H,[X,X'] ~2 Then exact the r - t o r s i o n sequence " O T h e n we get the s e q u e n c e > FD >> FA , ~i = ([I,i],-I ~ d ) with 1 = identity on C ~2 = (F(d) , [d,l]) with I = identity on D , FT(A) is ( 2.

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