A fake smooth $\Bbb{CP}^2\#\Bbb{RP}^4$

A Fake Smooth Cp#rp

We show that the manifold ∗CP# ∗RP, which is homotopy equivalent but not homeomorphic to CP#RP, is in fact smoothable.

A Fake Smooth Cp 2 #rp

We show that the manifold ∗RP# ∗CP, which is homotopy equivalent but not homeomorphic to RP#CP, is in fact smoothable.

Real Fake Real Fake

Fake!

Received: 3 October 2005 Accepted: 3 October 2005 One of my most memorable experiences with Claudio occured in Cleveland about 10 years ago. I was serving as department chair, and had organized a semester long research seminar, bringing one great scholar in for a full week, every week of the term. During their week in residence, the visitors would give two seminars and meet informally with facu...

Fake Variables in research

In each journal, the editorial board receives many articles but more than 70% of them are rejected. This happens because there is no real correlation among the variables in these articles or the variables and perceived relations are fake, which means playing with the variables nonexistent in reality. This rejection occurs mainly as a result of the researchers' misinterpretation of the interdisc...