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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeApr 22nd 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownSignificant improvements and expansion in [[determinant line bundle]] and new related stub [[analytic torsion]].

   Significant improvements and expansion in determinant line bundle and new related stub analytic torsion.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeApr 22nd 2010
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   Author: zskoda
   Format: MarkdownAnother radical expansion of [[determinant line bundle]].

   Another radical expansion of determinant line bundle.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeSep 3rd 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the actual definition at _[[analytic torsion]]_

   added the actual definition at analytic torsion

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 3rd 2014
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   Author: David_Corfield
   Format: MarkdownItexIn arithmetic topology it is claimed by [Morishita](http://arxiv.org/pdf/0904.3399.pdf?origin=publication_detail) that >the Iwasawa main conjecture, which relates Iwasawa polynomials with p-adic analytic zeta functions, may be seen as an analogue of the relation between Reidemeister torsions and analytic torsions. (p. 28)

   In arithmetic topology it is claimed by Morishita that

   the Iwasawa main conjecture, which relates Iwasawa polynomials with p-adic analytic zeta functions, may be seen as an analogue of the relation between Reidemeister torsions and analytic torsions. (p. 28)

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 3rd 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. I made a brief note on that at _[[analytic torsion]]_, need to look into it later. By the way, there is a vague similarity between [Reznikov's variant](http://ncatlab.org/nlab/show/arithmetic+topology#ReznikovVariant) of arithmetic topology and the [2-framings via cobounding 4-manifolds](http://ncatlab.org/nlab/show/2-framing#RelationToBounding4Manifolds) which appear in the definition of Chern-Simons theory. Given the general thrust of the analogy, this might be relevant, but I'd need to think more about it.

   Thanks. I made a brief note on that at analytic torsion, need to look into it later.

   By the way, there is a vague similarity between Reznikov’s variant of arithmetic topology and the 2-framings via cobounding 4-manifolds which appear in the definition of Chern-Simons theory.

   Given the general thrust of the analogy, this might be relevant, but I’d need to think more about it.

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 3rd 2014
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   Author: David_Corfield
   Format: MarkdownItexYou often see analytic torsion and eta invariant mentioned together. E.g., John Lott [says](http://math.berkeley.edu/~lott/lhouches.pdf) >They have the flavor of being “secondary” invariants. In recent years much progress has been made in making this precise, in showing how [they] arise via transgression from “primary” invariants. Presumably that's in the same sense of the secondary invariants of sec 3.1 of the Regensberg [proposal](http://www-app.uni-regensburg.de/Fakultaeten/MAT/GK/images/Vollantrag2.pdf).

   You often see analytic torsion and eta invariant mentioned together. E.g., John Lott says

   They have the flavor of being “secondary” invariants. In recent years much progress has been made in making this precise, in showing how [they] arise via transgression from “primary” invariants.

   Presumably that’s in the same sense of the secondary invariants of sec 3.1 of the Regensberg proposal.

7. • CommentRowNumber7.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 3rd 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexLott's clearer about the relationship [here](http://math.berkeley.edu/~lott/sec.pdf) where eta invariant and analytic torsion appear as analogues in Table 1.

   Lott’s clearer about the relationship here where eta invariant and analytic torsion appear as analogues in Table 1.

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeSep 3rd 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe closest relation that I am aware of is that when treating the Chern-Simons path integral in perturbation theory then it becomes a product of powers/exponentials of analytic torsion and the eta invariant. I had had dug out fairly good reviews of this late last night, but I lost the collected links this morning. The story is however already told by Witten in his original article ([here](http://projecteuclid.org/euclid.cmp/1104178138)): in (2.8) the determinant of the Laplace operator appears, then in (2.14) the eta invariant. The latter term is also discussed for instance in [Lott 90](http://ncatlab.org/nlab/show/eta+invariant#Lott90). I had some references that produced the full CS path integral expression including both the analytic torsion and the eta invariant more neatly. Will have to search for them again, though.

   The closest relation that I am aware of is that when treating the Chern-Simons path integral in perturbation theory then it becomes a product of powers/exponentials of analytic torsion and the eta invariant.

   I had had dug out fairly good reviews of this late last night, but I lost the collected links this morning.

   The story is however already told by Witten in his original article (here): in (2.8) the determinant of the Laplace operator appears, then in (2.14) the eta invariant. The latter term is also discussed for instance in Lott 90.

   I had some references that produced the full CS path integral expression including both the analytic torsion and the eta invariant more neatly. Will have to search for them again, though.

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeJan 24th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * [[Cumrun Vafa]], *Ray-Singer Torsion, Topological Strings and Black Holes* &lbrack;[arXiv:2401.12816](https://arxiv.org/abs/2401.12816)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/analytic+torsion/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/analytic+torsion/15">v15</a>, <a href="https://ncatlab.org/nlab/show/analytic+torsion">current</a>

   added pointer to today’s

   • Cumrun Vafa, Ray-Singer Torsion, Topological Strings and Black Holes [arXiv:2401.12816]

   diff, v15, current

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 23rd 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to today's * [[Matthias Blau]], Mbambu Kakona, [[George Thompson]], *On the Evaluation of the Ray-Singer Torsion Path Integral* &lbrack;[arXiv:2402.14437](https://arxiv.org/abs/2402.14437)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/analytic+torsion/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/analytic+torsion/16">v16</a>, <a href="https://ncatlab.org/nlab/show/analytic+torsion">current</a>

    added pointer to today’s

    • Matthias Blau, Mbambu Kakona, George Thompson, On the Evaluation of the Ray-Singer Torsion Path Integral [arXiv:2402.14437]

    diff, v16, current

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeFeb 23rd 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexand pointer to: * [[John Lott]], *The Ray-Singer torsion* &lbrack;[arXiv:2309.05688](https://arxiv.org/abs/2309.05688)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/analytic+torsion/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/analytic+torsion/16">v16</a>, <a href="https://ncatlab.org/nlab/show/analytic+torsion">current</a>

    and pointer to:

    • John Lott, The Ray-Singer torsion [arXiv:2309.05688]

    diff, v16, current