Self-intersections of immersions and Steenrod operations

Peter J. Eccles, Mark Grant

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We present a formula describing the action of a generalised Steenrod operation of Z(2)-type [14] on the cohomology class represented by a proper self-transverse immersion f: Ma dagger not signX. Our formula depends only on the Umkehr map, the characteristic 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 alpha is an element of H (k) (X; Z(2)) is the ordinary cohomology class represented by f: Ma dagger not signX, then Sq (i) (alpha) = f(*) w (i) (nu(f) ).

Original languageEnglish
Pages (from-to)272-281
Number of pages10
JournalActa Mathematica Hungarica
Volume137
Issue number4
Early online date3 Jan 2012
DOIs
Publication statusPublished - Dec 2012

Keywords

  • immersion
  • self-intersection
  • Steenrod-tom Dieck operation
  • Steenrod square
  • geometric cobordism

Cite this