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2012.34: SELF-INTERSECTIONS OF IMMERSIONS AND STEENROD OPERATIONS

2012.34: Peter J. Eccles and Mark Grant (2012) SELF-INTERSECTIONS OF IMMERSIONS AND STEENROD OPERATIONS. Acta Mathematica Hungarica. pp. 1-10. ISSN 1588-2632

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DOI: 10.1007/s10474-011-0189-9

Abstract

We present a formula describing the action of a gener- alised Steenrod operation of Z2-type [14] on the cohomology class represented by a proper self-transverse immersion f : M # X. Our formula depends only on the Umkehr map, the characteris- tic classes of the normal bundle, and the class represented by the double point immersion of f. This generalises a classical result of R. Thom [13]: If 2 Hk(X;Z2) is the ordinary cohomology class represented by f : M # X, then Sqi() = fwi(f ).

Item Type:Article
Uncontrolled Keywords:Immersion, Self-intersections, Steenrod-tom Dieck op- erations, Steenrod squares, geometric cobordism.
Subjects:MSC 2000 > 55 Algebraic topology
MSC 2000 > 57 Manifolds and cell complexes
MIMS number:2012.34
Deposited By:Ms Lucy van Russelt
Deposited On:18 March 2012

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