Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

October 13, 2009

Path-Structured Smooth (∞,1)-Toposes

Posted by Urs Schreiber

It seems that this Friday I’ll give a talk to the group of Ieke Moerdijk, where I just started a new position (as I mentioned).

Over on the nnLab I am preparing some notes along which such a talk might proceed:

Path-Structured Smooth (∞,1)(\infty,1)-Toposes (wiki page)

Abstract. A smooth topos is a context in which (synthetic) differential geometry exists. An (∞,1)(\infty,1)-topos is a context in which higher groupoids exist. Merging these two concepts yields the notion of a smooth (∞,1)(\infty,1)-topos: a context in which ∞\infty-Lie groupoids exist.

A lined topos is a context in which each space has a notion of path. A path-structured smooth (∞,1)(\infty,1)-topos is a context in which each ∞\infty-Lie groupoid comes with its smooth path ∞\infty-groupoid, naturally.

Path-structured and smooth (∞,1)(\infty,1)-toposes are the context in which gauge fields given by principal ∞\infty-bundles with connection exist.

Posted at October 13, 2009 1:15 AM UTC

TrackBack URL for this Entry:   https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2082



4 Comments & 0 Trackbacks

Re: Path-Structured Smooth (∞,1)-Toposes

Ah, so you’re no longer in Bonn?

Posted by: Kevin Lin on October 13, 2009 4:49 PM | Permalink | Reply to this

whereabouts

Ah, so you’re no longer in Bonn?

Currently I am oscillating back and forth. Luckily there is a good train connection.

I did certainly miss your GW-seminar today, unfortunately. I should be available at the elliptic seminar tomorrow, though.

Posted by: Urs Schreiber on October 13, 2009 5:08 PM | Permalink | Reply to this

Re: whereabouts

GW-seminar

That's a bad link; I don't know what it should be.

Posted by: Toby Bartels on October 13, 2009 11:35 PM | Permalink | Reply to this

entries on Gromov-Witten invariants

That’s a bad link;

Thanks for catching that. Fixed now.

I don’t know what it should be.

It was supposed to and now does point to the nnCafé entry called A Seminar on Gromov-Witten Invariants – whose point is to attract contributors to the entry nnLab:Gromov-Witten invariants.

Posted by: Urs Schreiber on October 14, 2009 10:03 AM | Permalink | Reply to this

Post a New Comment