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- Title
Free immersions and panelled web 4-manifolds.
- Authors
Kalafat, Mustafa
- Abstract
We show that if a compact, oriented 4-manifold admits a coassociative(∗ ϕ 0 )-free immersion into ℝ 7 , then its Euler characteristic χ M and signature τ M vanish. Moreover, in the spin case, the Gauss map is contractible, so that the immersed manifold is parallelizable. The proof makes use of homotopy theory, in particular, obstruction theory. As a further application, we prove a non-existence result for some infinite families of 4-manifolds that have not been addressed previously. We give concrete examples of parallelizable 4-manifolds with complicated non-simply-connected topology.
- Subjects
IMMERSIONS (Mathematics); DIFFERENTIABLE manifolds; FOUR-manifolds (Topology); HOMOTOPY theory; OBSTRUCTION theory
- Publication
International Journal of Mathematics, 2018, Vol 29, Issue 14, pN.PAG
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X18500878