Abstract
If a numerical homotopy invariant of finite simplicial complexes has a local formula, then, up to multiplication by an obvious constant, the invariant is the Euler characteristic. Moreover, the Euler characteristic itself has a unique local formula.
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References
Cheeger, J., Spectual geometry of singular Riemannian spaces,J. Differential Geom. 18 (1983), 575–657.
Gelfand, I. M., and MacPherson, R., A combinatorial formula for the Pontrjagin classes (preprint).
Klee, V., A combinatorial analogue of Poincaré's duality theorem,Canad. J. Math. 16 (1964), 517–531.
Levitt, N.,Grassmannians and Gauss Maps in Piecewise-Linear Topology, Lecture Notes in Mathematics, Vol. 1366, Springer-Verlag, Berlin, 1989.
Levitt, N., and Rourke, C., The existence of combinatorial formulae for characteristic classes,Trans. Amer. Math. Soc. 239 (1978), 391–397.
Steenrod, M., Cooke, G., and Finney R.,Homology of Cell Complexes, Princeton University Press, Princeton, NJ, 1967.
Wall, C. T. C., Classification problems in differential topology, IV—Thickenings,Topology 5 (1966), 73–94.
Wall, C. T. C., Arithmetic invariants of subdivisions of complexes,Canad. J. Math. 18 (1966), 72–96.
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Levitt, N. The euler characteristic is the unique locally determined numerical homotopy invariant of finite complexes. Discrete Comput Geom 7, 59–67 (1992). https://doi.org/10.1007/BF02187824
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DOI: https://doi.org/10.1007/BF02187824