The homotopy type of the space of maps of a homology 3-sphere into the 2-sphere

V. L. (Vagn Lundsgaard) Hansen

Vol. 76 (1978), No. 1, 43–49

DOI: 10.2140/pjm.1978.76.43

Abstract

It is proved that if K is a compact, connected polyhedron such that H²(K;Z) = 0, then all the components in the space of maps of K into the 2-sphere are homeomorphic. For K a polyhedral homology 3-sphere the common homotopy type of the components is identified and shown to be independent of K.

Mathematical Subject Classification 2000

Primary: 58D15

Secondary: 54C35, 55P99

Milestones

Received: 19 January 1977

Revised: 14 October 1977

Published: 1 May 1978