Bordism groups of immersions and classes represented by self-intersections

Eccles, Peter J and Grant, Mark (2006) Bordism groups of immersions and classes represented by self-intersections. [MIMS Preprint]

[img] PDF
ecclesgrant.pdf

Download (177kB)

Abstract

A well-known formula of R.J. Herbert's relates the various homology classes represented by the self-intersection immersions of a self-transverse immersion. We prove a geometrical version of Herbert's formula by considering the self-intersection immersions of a self-transverse immersion up to bordism. This clarifies the geometry lying behind Herbert's formula and leads to a homotopy commutative diagram of Thom complexes. It enables us to generalise the formula to other homology theories. The proof is based on Herbert's but uses the relationship between self-intersections and stable Hopf invariants and the fact that bordism of immersions gives a functor on the category of smooth manifolds and proper immersions.

Item Type: MIMS Preprint
Uncontrolled Keywords: immersions, bordism, cobordism, Herbert's formula
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology
MSC 2010, the AMS's Mathematics Subject Classification > 57 Manifolds and cell complexes
Depositing User: Dr Peter J Eccles
Date Deposited: 20 Dec 2006
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/674

Actions (login required)

View Item View Item