Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Geometric Topology

arXiv:0710.2681 (math)
[Submitted on 14 Oct 2007 (v1), last revised 5 Dec 2007 (this version, v2)]

Title:Multiplicative properties of Morin maps

Authors:Gabor Lippner, Andras Szucs
View PDF
Abstract: In the first part of the paper we construct a ring structure on the rational cobordism classes of Morin maps (i. e. smooth generic maps of corank 1). We show that associating to a Morin map its singular strata defines a ring homomorphism to $\Omega_* \otimes \Q$, the rational oriented cobordism ring. This is proved by analyzing multiple-point sets of product immersion. Using these homomorphisms we are able to identify the ring of Morin maps.
In the second part of the paper we compute the oriented Thom polynomial of the $\Sigma^2$ singularity type with $\Q$ coefficients. Then we provide a product formula for the $\Sigma^2$ and the $\Sigma^{1,1}$ singularities.
Comments: Corrected some small misprints and made lot of minor (mainly grammatical) alterations. 10 pages
Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT)
MSC classes: 57R45
Cite as: arXiv:0710.2681 [math.GT]
  (or arXiv:0710.2681v2 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.0710.2681
Journal reference: Algebr. Geom. Topol. 10 (2010) 1437-1454
Related DOI: https://doi.org/10.2140/agt.2010.10.1437

Submission history

From: Gabor Lippner [view email]
[v1] Sun, 14 Oct 2007 17:50:44 UTC (22 KB)
[v2] Wed, 5 Dec 2007 22:42:42 UTC (22 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.GT
< prev   |   next >
new | recent | 2007-10
Change to browse by:
math
math.AT

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)