English

Formality of certain CW complexes

Algebraic Topology 2018-08-21 v3

Abstract

Let XX be a simply connected path connected topological space which is formal in the sense of rational homotopy theory. Let Y=XαDnY=X\cup_\alpha\mathbb{D}^{n} where α:Sn1X\alpha:\mathbb{S}^{n-1}\to X is a non-torsion element. Then we obtain a condition on α\alpha for the formality of YY. We give several illustrative examples concerning the formality of a finite CW complex having only even dimensional cells. This is the corrected version of the earlier version which contained a serious error in Theorem 1.4. This theorem, which now Theorem 1.1 of this version, has now been corrected. The proofs of Theorems 1.1, 1.2, and 1.3 of the first version are not valid as they used the erroneous result. In fact, we provide here a counterexample to the assertion of Theorem 1.1. (See Example 3.1 below.) We do not know if the statement of Theorem 1.2, which asserted the formality of Schubert varieties in a generalized flag variety G/BG/B, is valid. Theorem 1.3 is correct as stated as it had been proved previously by Panov and Ray using entirely different techniques.

Keywords

Cite

@article{arxiv.1301.5421,
  title  = {Formality of certain CW complexes},
  author = {Prateep Chakraborty and Parameswaran Sankaran},
  journal= {arXiv preprint arXiv:1301.5421},
  year   = {2018}
}

Comments

This is the corrected version of previous submission

R2 v1 2026-06-21T23:13:59.170Z