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2006.418: Bordism groups of immersions and classes represented by self-intersections

2006.418: Peter J Eccles and Mark Grant (2006) Bordism groups of immersions and classes represented by self-intersections.

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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 2000 > 55 Algebraic topology
MSC 2000 > 57 Manifolds and cell complexes
MIMS number:2006.418
Deposited By:Dr Peter J Eccles
Deposited On:20 December 2006

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