Geodesic
Multiplicative properties of Morin maps
Lippner, Gábor1 ; Szűcs, András2
1Department of Mathematics, Harvard University, One Oxford Street, Cambridge 02138, United States
2Department of Analysis, Eotvos University, Pazmany Peter setany 1/c, Budapest, 1117, Hungary
Algebraic and Geometric Topology, Tome 10 (2010) no. 3, pp. 1437-1454
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In the first part of the paper we construct a ring structure on the rational cobordism classes of Morin maps (ie smooth generic maps of corank 1). We show that associating to a Morin map its Σ1r (or Ar) singular strata defines a ring homomorphism to Ω∗⊗ ℚ, the rational oriented cobordism ring. This is proved by analyzing the multiple-point sets of a product immersion. Using these homomorphisms we compute the ring of Morin maps.

In the second part of the paper we give a new method to find the oriented Thom polynomial of the Σ2 singularity type with ℚ coefficients. Then we provide a product formula for the Σ2 singularity in ℚ and the Σ1,1 singularity in ℤ2 coefficients.

DOI : 10.2140/agt.2010.10.1437
Keywords: product map, Morin singularity

Lippner, Gábor  1   ; Szűcs, András  2

1 Department of Mathematics, Harvard University, One Oxford Street, Cambridge 02138, United States
2 Department of Analysis, Eotvos University, Pazmany Peter setany 1/c, Budapest, 1117, Hungary 
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Lippner, Gábor; Szűcs, András. Multiplicative properties of Morin maps. Algebraic and Geometric Topology, Tome 10 (2010) no. 3, pp. 1437-1454. doi: 10.2140/agt.2010.10.1437

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