Nonexistence of almost complex structures on the product S^2m × M

Authors

Prateep Chakraborty, Indian Statistical Institute Bangalore
Ajay Singh Thakur, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Topology and its Applications

Abstract

In this note we give a necessary condition for having an almost complex structure on the product S2m × M, where M is a connected orientable closed manifold. We show that if the Euler characteristic χ(M) ≠ 0, then except for finitely many values of m, we do not have almost complex structure on S2m × M. In the particular case when M=CPn, n ≠ 1, we show that if n≢3(mod4) then S2m × CPn has an almost complex structure if and only if m=1, 3. As an application we obtain conditions on the nonexistence of almost complex structures on Dold manifolds.

First Page

102

Last Page

110

DOI

10.1016/j.topol.2015.12.057

Publication Date

2-15-2016

Comments

Open Access; Bronze Open Access

Recommended Citation

Chakraborty, Prateep and Thakur, Ajay Singh, "Nonexistence of almost complex structures on the product S^2m × M" (2016). Journal Articles. 4319.
https://digitalcommons.isical.ac.in/journal-articles/4319