Volume 10, issue 3 (2010)

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Multiplicative properties of Morin maps

Gábor Lippner and András Szűcs

Algebraic & Geometric Topology 10 (2010) 1437–1454

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.

product map, Morin singularity
Mathematical Subject Classification 2000
Primary: 57R20, 57R42, 57R45
Received: 8 August 2008
Revised: 19 May 2010
Accepted: 20 May 2010
Published: 1 July 2010
Gábor Lippner
Department of Mathematics
Harvard University
One Oxford Street
Cambridge 02138
United States
András Szűcs
Department of Analysis
Eotvos University
Pazmany Peter setany 1/c