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This manual documents the KSPACE library, a C++ suite that uses the GNU MP arbitrary precision arithmetic package, and J. Wilkening's GMPFRXX C++ wrapper, to compute the Kreck-Stolz invariants of a class of Eschenburg spaces.
Aloff and Wallach introduced a family of homogeneous spaces of SU(3); Eschenburg generalised this construction to construct biquotients of SU(3). Kreck and Stolz studied the homeomorphism and diffeomorphism classification of AW spaces and showed the existence of a pair that are homeomorphic but not diffeomorphic. Kruggel showed how to compute the KS invariants of certain Eschenburg spaces (after Astey, Micha and Pastor had done so for a class with free S^1 actions). Chinburg, Escher and Ziller computed these invariants numerically and found examples of homeomorphic, but not diffeomorphic, Eschenburg spaces that are positively-curved or 3-Sasakian.
The present library has been used to show that many homeomorphism classes of Eschenburg-Kruggel spaces have all 28 smooth structures represented by Eschenburg-Kruggel spaces.
The present manual documents the software used in the paper Smooth structures on Eschenburg spaces: numerical computations. The paper is available from http://erdelyi.maths.ed.ac.uk/~lbutler/preprint.html.
KSPACE infrastructure
--- The Detailed Node Listing ---
Introduction
Build