Volume 10, issue 3 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Multiplicative properties of Morin maps

Gábor Lippner and András Szűcs

Algebraic & Geometric Topology 10 (2010) 1437–1454
Abstract

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.

Keywords
product map, Morin singularity
Mathematical Subject Classification 2000
Primary: 57R20, 57R42, 57R45
References
Publication
Received: 8 August 2008
Revised: 19 May 2010
Accepted: 20 May 2010
Published: 1 July 2010
Authors
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
Budapest
1117
Hungary