Self-intersections of Immersions and Steenrod Operations

2005/09/09 by Peter J. Eccles, Eccles, Peter J., Mark Grant +1 · 1 citation
Mathematics · Physics and Astronomy · #55N22 #55S25 (Secondary) #57R19 (Primary) #57R42 #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AT #math.MP #msc:55N22 #msc:55S25 #msc:57R19 #msc:57R42

paper · pdf · doi:10.48550/arxiv.math/0509213

10 pages; v3 final version, to appear in Acta Math. Hungarica

arxiv created 2011/09/26 · arxiv updated 2011/09/27

Abstract

We present a formula describing the action of a generalised Steenrod operation of \Z₂-type on the cohomology class represented by a proper self-transverse immersion f\co M\imm X, in terms of the equivariant double points of f and the characteristic classes of its normal bundle. This generalises a classical result of R. Thom: If α∈ H^k(X;\Z₂) is the ordinary cohomology class represented by f\co M\imm X, then Sqⁱ(α)=f_* w_i(ν_f).

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