**
MATHEMATICA BOHEMICA, Vol. 132, No. 1, pp. 59-74 (2007)
**

#
Properties of a hypothetical exotic complex structure on $\Bbb C P^3$

##
J. R. Brown

* J. Ryan Brown*, Georgia College & State University, Department of Mathematics, CBX 017, Milledgeville, GA 31061, USA, e-mail: ` ryan.brown@gcsu.edu`

**Abstract:** We consider almost-complex structures on $\mathbb {C}\text P^3$ whose total Chern classes differ from that of the standard (integrable) almost-complex structure. E. Thomas established the existence of many such structures. We show that if there exists an "exotic" integrable almost-complex structures, then the resulting complex manifold would have specific Hodge numbers which do not vanish. We also give a necessary condition for the nondegeneration of the Frölicher spectral sequence at the second level.

**Keywords:** complex structure, projective space, Frölicher spectral sequence, Hodge numbers

**Classification (MSC2000):** 53C56, 53C15, 58J20, 55T99

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number] [Journals Homepage]

*
© 2007–2010
FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
*