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We classify the most common local forms of smooth maps from a smooth manifold L to the plane. The word local can refer to locations in the source L, but also to locations in the target. The first point of view leads us to a classification of certain germs of maps, which we review here although it is very well known. The second point of view leads us to a classification of certain multigerms of maps.
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Rui Reis, Michael S. Weiss, Smooth maps to the plane and Pontryagin classes. Part I: Local aspects. Port. Math. 69 (2012), no. 1, pp. 41–67DOI 10.4171/PM/1904