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2010 Multiplicative properties of Morin maps
Gábor Lippner, András Szűcs
Algebr. Geom. Topol. 10(3): 1437-1454 (2010). DOI: 10.2140/agt.2010.10.1437


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, 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 coefficients. Then we provide a product formula for the Σ2 singularity in and the Σ1,1 singularity in 2 coefficients.


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Gábor Lippner. András Szűcs. "Multiplicative properties of Morin maps." Algebr. Geom. Topol. 10 (3) 1437 - 1454, 2010.


Received: 8 August 2008; Revised: 19 May 2010; Accepted: 20 May 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1200.57023
MathSciNet: MR2661533
Digital Object Identifier: 10.2140/agt.2010.10.1437

Primary: 57R20 , 57R42 , 57R45

Keywords: Morin singularity , product map

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.10 • No. 3 • 2010
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