NDLI: The geometric Hopf invariant and double points

Content Provider	Springer Nature Link
Author	Crabb, Michael Ranicki, Andrew
Copyright Year	2010
Abstract	The geometric Hopf invariant of a stable map F is a stable $${{\mathbb Z}/2}$$ -equivariant map h(F) such that the stable $${{\mathbb Z}/2}$$ -equivariant homotopy class of h(F) is the primary obstruction to F being homotopic to an unstable map. In this paper, we express the geometric Hopf invariant of the Umkehr map F of an immersion $${f : M^m \looparrowright N^n}$$ in terms of the double point set of f. We interpret the Smale–Hirsch–Haefliger regular homotopy classification of immersions f in the metastable dimension range 3m < 2n – 1 (when a generic f has no triple points) in terms of the geometric Hopf invariant.
Starting Page	325
Ending Page	350
Page Count	26
File Format	PDF
ISSN	16617738
Journal	Journal of Fixed Point Theory and Applications
Volume Number	7
Issue Number	2
e-ISSN	16617746
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2010-08-21
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometric Hopf invariant immersion double point Hopf invariants Immersions Mathematical Methods in Physics Analysis Mathematics
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Modeling and Simulation

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The geometric Hopf invariant and double points