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Minimizing coincidence in positive codimension

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Abstract

Let f and g be maps between smooth manifolds M and N of dimensions n + m and n, respectively (where m > 0 and n > 2). Suppose that the image (fxg)(M) intersects the diagonal N × N in finitely many points, whose preimages are smooth m-submanifolds inM. The problem of minimizing the coincidence set Coin(f, g) of the maps f and g with respect to these preimages and/or their components is considered. The author’s earlier results are strengthened. Namely, sufficient conditions under which such a coincidence m-submanifold can be removed without additional dimensional constraints are obtained.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    T. N. Fomenko

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  1. T. N. Fomenko
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Correspondence to T. N. Fomenko.

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To the blessed memory of my dear teacher Yurii Grigor’evich Borisovich (1930–2007)

Original Russian Text © T. N. Fomenko, 2008, published in Matematicheskie Zametki, 2008, Vol. 84, No. 3, pp. 440–451.

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Fomenko, T.N. Minimizing coincidence in positive codimension. Math Notes 84, 407–416 (2008). https://doi.org/10.1134/S0001434608090113

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  • DOI: https://doi.org/10.1134/S0001434608090113

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