A fake smooth CP^2 # RP^4

TL;DR

This paper proves that the manifold *CP^2 # *RP^4, which is homotopy equivalent but not homeomorphic to CP^2 # RP^4, admits a smooth structure, resolving a question about its smoothability.

Contribution

It demonstrates the smoothability of a specific exotic manifold, *CP^2 # *RP^4, which was previously known only to be homotopy equivalent but not homeomorphic to the standard connected sum.

Findings

The manifold *CP^2 # *RP^4 is smoothable.

It is homotopy equivalent but not homeomorphic to CP^2 # RP^4.

The result clarifies the smooth structure of this exotic manifold.

Abstract

We show that the manifold *CP^2 # *RP^4, which is homotopy equivalent but not homeomorphic to CP^2 # RP^4, is in fact smoothable.