The primary role played by analogy in Henri Poincaré’s work, and in particular in his “analysis situs” papers, is emphasized. Poincaré’s “sixth example” (showing that Betti numbers do not suffice to classify 3-manifolds) and his construction of the homology sphere are discussed in detail.
Analogy and invention. Some remarks on Poincaré’s Analysis situs papers
BARTOCCI, CLAUDIO
2018-01-01
Abstract
The primary role played by analogy in Henri Poincaré’s work, and in particular in his “analysis situs” papers, is emphasized. Poincaré’s “sixth example” (showing that Betti numbers do not suffice to classify 3-manifolds) and his construction of the homology sphere are discussed in detail.
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