Abstract
Consider the following statements :
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1.
If f :S2 → ℝ2 is C1 then f-1 (y) is finite for “most“ points y ∈ ℝ.
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2.
Two lines in ℝ3 do not intersect “in general.“
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3.
If f: ℝ→ ℝ is C1, “almost all“ horizontal lines in ℝ × ℝ are nowhere tangent to the graph of f.
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4.
“Generically“ a C1 immersion S1 → ℝ2 has only a finite number of crossing points.
Transversality unlocks the secrets of the manifold.
H. E. Winkelnkemper
“Transversal“ is a noun; the adjective is “transverse.“
J. H. C. Whitehead, 1959
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© 1976 Springer-Verlag New York Inc.
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Hirsch, M.W. (1976). Transversality. In: Differential Topology. Graduate Texts in Mathematics, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9449-5_4
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DOI: https://doi.org/10.1007/978-1-4684-9449-5_4
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