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2007 Bordism groups of immersions and classes represented by self-intersections
Peter J Eccles, Mark Grant
Algebr. Geom. Topol. 7(2): 1081-1097 (2007). DOI: 10.2140/agt.2007.7.1081


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.


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Peter J Eccles. Mark Grant. "Bordism groups of immersions and classes represented by self-intersections." Algebr. Geom. Topol. 7 (2) 1081 - 1097, 2007.


Received: 20 December 2006; Revised: 30 March 2007; Accepted: 5 April 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1136.57016
MathSciNet: MR2336250
Digital Object Identifier: 10.2140/agt.2007.7.1081

Primary: 57R42
Secondary: 55N22, 57R90

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.7 • No. 2 • 2007
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