An integer equal to 0 or 1 which vanishes iff the product manifold can be given a smooth structure. Here, is a compact connected topological four-manifold.
Kirby-Siebenmann Invariant
See also
Smale TheoremExplore with Wolfram|Alpha
References
Freedman, M. H. and Quinn, F. Topology of 4-Manifolds. Princeton, NJ: Princeton University Press, 1990.Kirby, R. C. and Siebermann, L. C. Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. Princeton, NJ: Princeton University Press, 1977.Referenced on Wolfram|Alpha
Kirby-Siebenmann InvariantCite this as:
Weisstein, Eric W. "Kirby-Siebenmann Invariant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kirby-SiebenmannInvariant.html