Cohomotopy sets of 4-manifolds

Details Cohomotopy sets of 4-manifolds Cohomotopy sets of 4-manifolds

2012-03-07

arxiv.org/abs/1203.1608v1

Mathematics

Geometric Topology

20 pages, 6 figures

Scientific paper

Elementary geometric arguments are used to compute the group of homotopy classes of maps from a 4-manifold X to the 3-sphere, and to enumerate the homotopy classes of maps from X to the 2-sphere. The former completes a project initiated by Steenrod in the 1940's, and the latter provides geometric arguments for and extensions of recent homotopy theoretic results of Larry Taylor. These two results complete the computation of all the cohomotopy sets of closed oriented 4-manifolds and provide a framework for the study of Morse 2-functions on 4-manifolds, a subject that has garnered considerable recent attention.

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