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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 22nd 2011
• (edited Mar 22nd 2011)

have expanded the first section at determinant line bundle. Spelled out some more details and then stated the fact that the class of the determinant line bundle of a complex vector bundle is its first Chern-class, and that this statement directly refines to differential cohomology.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeMar 22nd 2011

Hi Urs! I like that you joined the work on this important entry. I started doing this a while ago, but stayed rather cryptic. Now you are bringing some real explanations to it :)

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 22nd 2011
• (edited Mar 22nd 2011)

I wanted to mention the example $det$ tomorrow for a talk on differential characteristic classes that I give in Rome, as a very simple and yet insightful example for a characteristic class and was surprised that the evident statement $[det E] = c_1(E)$ for a complex vector bundle $E$ is so hard to find explicitly in the basic literature. One finds plenty of generalized versions of this statement, but for expositional purposes I wanted just this bare one. Thanks to Domenico for tracking down references!

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeSep 11th 2014

I have cross-linked determinant line bundle and theta function a bit more (and vacuum energy) by pointing to (Freed 87, pages 30-31)

(no time for more than just these pointers right now)

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJul 20th 2022

Where the entry used to be vaguley referring to induced fiberwise operations (here) I have added a pointer to the new Remark on these at topological vector bundle, here.

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