## Tsukuba Journal of Mathematics

### Remarks on the bordism intersection map

#### Abstract

In this paper we give a characterization of the kernel of the bordism intersection map and we present some related results as the following. The set of bordism classes of $C^{\infty}$ maps $f : M \to N$ such that rank $df(x) \leq p$ for all $x$ is contained in $J_{p,m-p}(N)$, where $M$ is a smooth closed manifold of dimension $m$, $N$ is a smooth closed manifold, $df$ is the differential of $f$, $J_{p,m-p}(N)$ is the image of the homomorphism $\ell_{\ast}: \mathfrak{N}_{m}(N^{(p)}) \to \mathfrak{N}_{m}(N)$ induced by the inclusion, $0 \leq p \leq m$, and $N^{(p)}$ is the $p$-skeleton of $N$.

#### Article information

Source
Tsukuba J. Math., Volume 30, Number 1 (2006), 171-180.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496165035

Digital Object Identifier
doi:10.21099/tkbjm/1496165035

Mathematical Reviews number (MathSciNet)
MR2248290

Zentralblatt MATH identifier
1115.55003

#### Citation

Biasi, Carlos; Libardi, Alice Kimie Miwa. Remarks on the bordism intersection map. Tsukuba J. Math. 30 (2006), no. 1, 171--180. doi:10.21099/tkbjm/1496165035. https://projecteuclid.org/euclid.tkbjm/1496165035