Abstract
We now have enough machinery at our disposal to develop one of the most important tools in topology: the degree of a map f: M → N, where M and N are compact n-manifolds, N is connected, and ∂M = ∂N = Ø. This degree is an integer if M and N are oriented, an integer mod 2 otherwise.
Topology has the peculiarity that questions belonging in its domain may under certain circumstances be decidable even though the continua to which they are addressed may not be given exactly, but only vaguely, as is always the case in reality.
H. Weyl, Philosophy of Mathematics and Natural Science, 1949
Geometry is a magic that works ...
R. Thorn, Stabilité Structurelle et Morphogenese, 1972
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© 1976 Springer-Verlag New York Inc.
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Hirsch, M.W. (1976). Degrees, Intersection Numbers, and the Euler Characteristic. In: Differential Topology. Graduate Texts in Mathematics, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9449-5_6
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DOI: https://doi.org/10.1007/978-1-4684-9449-5_6
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