Links of singularities up to regular homotopy

Journal of Singularities
volume 10 (2014), 174-182

Received 3 February 2013. Received in revised form 6 August 2013.

DOI: 10.5427/jsing.2014.10k

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Abstract:

We classify links of the singularities x^2 + y^2 + z^2 + v^{2d} = 0 in (C^4, 0) up to regular homotopies precomposed with diffeomorphisms of S^3 x S^2. Let us denote the link of this singularity by L_d and denote by i_d the inclusion of L_d into S^7. We show that for arbitrary diffeomorphisms \varphi_d:S^3 x S^2 -> L_d the compositions i_d with \varphi_d are image regularly homotopic for two different values of d, d = d_1 and d = d_2, if and only if d_1 is congruent to d_2 mod 2.

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