Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bordism groups of special generic mappings


Author: Rustam Sadykov
Journal: Proc. Amer. Math. Soc. 133 (2005), 931-936
MSC (2000): Primary 55N22; Secondary 55P42, 57R45
Published electronically: August 24, 2004
MathSciNet review: 2113946
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Pontrjagin-Thom construction expresses a relation between the oriented bordism groups of framed immersions $M^m\looparrowright \mathbb{R} ^n, m<n$, and the stable homotopy groups of spheres. We apply the Pontrjagin-Thom construction to the oriented bordism groups $\mathcal M_{m,n}$ of mappings $M^m\to \mathbb{R} ^n, m>n$, with mildest singularities. Recently, O. Saeki showed that for $m\ge 6$, the group $\mathcal M_{m,1}$ is isomorphic to the group of smooth structures on the sphere of dimension $m$. Generalizing, we prove that $\mathcal M_{m,n}$ is isomorphic to the $n$-th stable homotopy group $\pi^{st}_n( \mathrm{BSDiff}_r,\mathrm{BSO}_{r+1})$, $r=m-n$, where $\mathrm{SDiff}_r$ is the group of oriented auto-diffeomorphisms of the sphere $S^{r}$ and $\mathrm{SO}_{r+1}$ is the group of rotations of $S^r$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55N22, 55P42, 57R45

Retrieve articles in all journals with MSC (2000): 55N22, 55P42, 57R45


Additional Information

Rustam Sadykov
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07586-0
PII: S 0002-9939(04)07586-0
Keywords: Pontrjagin-Thom construction, special generic mappings, bordisms
Received by editor(s): August 14, 2003
Received by editor(s) in revised form: November 10, 2003
Published electronically: August 24, 2004
Communicated by: Paul Goerss
Article copyright: © Copyright 2004 American Mathematical Society