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

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

Example text

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. Standard constructions: IT11 × IT21 ~ cartesian and of IT 1 × T21 product t2 J s2 ITII of as and T 1 × T2 T2 T2 the partially with "(tl,t2) IT21 with T l .

A tessel- with a pl-homeomorph- IT]o T = {(al, ~o o,an) Examples: if and only if ] a i 6 {O,I , 2}} (a i - bi)(b i - l) = 0 lation of the n-dimensional cube tjo,j I =: {(x I ..... x n) I In E xj = 0 for any pair of disjoint (Jo,Jl) • ) In the definition t < s ~ s = t"o for all with "(a| ,~oo 'an) < (b] ,o °°' b n )" i = I ..... n gives the standard tessel- In; the "tile" for subsets of a partially j C Jo' xj = i of ordered [I ..... n} for j 6 Jl } which and of dimension set we include the axiom is defined n-iJoI-[JiI "s j t and 57 corresponds to aj = I j C {I .....

IM N I,M O g O O O IM f',0 I'M N II I/i c-t.. oo I~1 c+ i! cn o I,M o O i',,o I'M N -1 IM IM I'M O H- IM IM IM IM O IM "-'1 I'M "~ I£:1 V 11 II V IM o I~O I'M N -I~ I'M N r,,o I'M N . . . . rl 52 X X9(P,t) X11(r,t) X10(r) Y Z/2®Z/2 Z/2 0 Z/p t 11 Z/2 r+1 Z Z/2 t 0 Z/21'eZ/2 0 0 0 m/p t Z Z/2 t 0 Z/2 m+l z / 2 n " e Z / 2 m+1 0 Z/2 m' Zl2nmz/2 m' Z/g n 10 Z/2 r + l Zip t E/21'~Z/2®Z/2 0 0 ZmZ/2 I ' r'~r" r'>r" Z / 2 1 ' e Z / 2 m+l r'~r^t'~t: r'>rvt' > Aut X ~ Aut Z/2 t+1 eAut(Z/2 r+1) w h i c h is split if r ~ t.

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