Smooth structures on Eschenburg spaces: numerical computations
Leo T. Butler
TL;DR
This paper uses numerical methods to compute topological and smooth invariants of Eschenburg spaces, focusing on those with small fourth cohomology, and employs high-precision computations to verify invariants.
Contribution
It provides a numerical approach to determine invariants of Eschenburg spaces, extending prior theoretical results with explicit computations.
Findings
Computed invariants for specific Eschenburg spaces
Verified Kreck-Stolz invariants numerically
Demonstrated the effectiveness of high-precision computations
Abstract
This paper numerically computes the topological and smooth invariants of Eschenburg spaces with small fourth cohomology group, following Kruggel's determination of the Kreck-Stolz invariants of Eschenburg spaces that satisfy condition C. The GNU GMP arbitrary-precision library is utilised.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology