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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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
|Deposited By:||Dr Peter J Eccles|
|Deposited On:||20 December 2006|