### Literature on Exotic R4s

#### Posted by Urs Schreiber

Today I received the following question by Florent Dieterlen on exotic ${\mathbb{R}}^{4}$ spaces. Since I am no expert on exotic spaces and cannot readily answer this question I reproduce it here in public (with kind permission). If anyone feels like providing help, please do so.

Hello,

I saw your discussion on a forum about exotic ${\mathbb{R}}^{4}$s. I was brought up as a physicist, but did not practice since, except for dynamical systems. I want to study exotic ${\mathbb{R}}^{4}$s, to be able to construct some, following certain conditions from an application. It is not properly a physics application. The problem is that i don’t have the basics. So my question is: starting from level MSc in physics, how do i get the most efficiently to the level i want:

1) do i have to follow Seiberg-Witten instead of Donaldson? The basics are not completely the same.

2) do you counsel Nash and Sen instead of Nakahara for the basics, if i want something very intuitive?

3) If 1) is yes, what book do you counsel for the study of exotic ${\mathbb{R}}^{4}$s following Seiberg-Witten?

Posted at September 27, 2005 6:03 PM UTCThanks in advance for your answer,

Best regards,

Florent Dieterlen

## Re: Literature on Exotic R4s

I would ask Hendryk Pfeiffer (now in Golm) who has thought about this problem a lot.

You should be warned that this is non-trivial and requires some elaborate theory. And when mathematicians say ‘Seiberg-Witten theory’ it looks completely different from what physicists think its about (N=2 gauge theory). Of course, in the end, it’s the same but that is by no means obvious.