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Paper   IPM / M / 17393
School of Mathematics
  Title:   Bordism class of multiple point manifolds of certain immersions
  Author(s):  Hadi Zare (Joint with Kh. Ghasemi and A. S. Janfada)
  Status:   Published
  Journal: Bol. Soc. Mat. Mex.
  Vol.:  29
  Year:  2023
  Pages:   1-13
  Supported by:  IPM
For a given immersion $M^7\looparrowright{\mathbb R}^8$, we completely determine bordism class of its self-intersection manifolds. This is done by computing the image of the unstable Hurewicz homomorphism $$h:\pi_8^s{\mathbb R} P^\infty\simeq \pi_8Q{\mathbb R} P^\infty\to H_8(Q{\mathbb R} P^\infty;{\mathbb Z}/2)$$ and applying formulae of Asadi-Golmankhaneh and Eccles.

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