By Lowell Jones
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Extra info for Combinatorial Symmetries of the M-Dimensional Ball
6N ) (K) is a Z(n)-homological sphere. -homology as a sphere minus r points. i (If M. -homology as a COMBINATORIAL SYMMETRIES OF THE m-DIMENSIONAL BALL (e) 53 (F |6N ) _ 1 ( b o ) * * i £ 6 N 1 * 0 ; ( F |N ) _ 1 ( b o ) * 0 i £ Nl * 0 ; -1 -1 -1 both CFi 6 N ) (b Q ) and (F>N ) (b Q ) - (F| 6 N ) (b Q ) are path connected. Here b = KDe, where e is the cell in R denoted by b-(R) in section 1. 4 when M. is a manifold. Transversality techniques show that the bordism class represented by g^;:: M. "> * RR/ / R corresponds to an element [g.
UN, set gt: M! -> R/R equal g-Ug. 4(a), (b),(c),(d). 4(a)-(d), where p: Nx[0,l] •> N is the projection. Set FM = F' u-g°p. Choose a smooth cobordism H: W -> R/R with 3_H = g. and 8+H = a_F", so that the transversalities of 8+H to the simplices of K^ ^ is extended to all of H. Define F = HuF" where the union occurs along the identification a+H = a F1. 4(a)-(d). 4(e) is true during the surgery process of the above proof (see COMBINATORIAL SYMMETRIES OF THE m-DIMENSIONAL BALL 57 (see [,§2]). 4 when M.
9. (R) is a cell. 1, consider the map p: L^(R,Zn) -> L^(R,Zn) defined by forming the cartesian product g -* g x (CP2)2 , where £ represents an element 3 G L (R,Z ) , CP and <£ x (CP ) 2 is 2 dimensional complex projective space, represents an element p(3) e Lg(R,Z ) . 9 in  is easily generalized to show that p is an isomorphism. ZJ. The maps a,p have been shown to be isomorphisms so A is an isomorphism. 1. 2: and q € H. Let H denote any path connected commutative H-space, The fundamental group TT-.
Combinatorial Symmetries of the M-Dimensional Ball by Lowell Jones