Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Spectral flow as winding number and integral formulas

Author(s): Charlotte Wahl
Journal: Proc. Amer. Math. Soc. 135 (2007), 4063-4073.
MSC (2000): Primary 58J30; Secondary 47B10
Posted: September 12, 2007
MathSciNet review: 2341959
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: A general integral formula for the spectral flow of a path of unbounded selfadjoint Fredholm operators subject to certain summability conditions is derived from the interpretation of the spectral flow as a winding number.

References:

[APS]
M.F. Atiyah, V.K. Patodi and I.M. Singer, ``Spectral asymmetry and Riemannian geometry III'', Math. Proc. Cambridge Philos. Soc. 79 (1976), no. 1, pp. 71-99. MR 0397799 (53:1655c)

[ASS]
S. Avron, R. Seiler and B. Simon, ``The index of a pair of projections'', J. Funct. Anal. 120 (1994), no. 1, pp. 220-237. MR 1262254 (95b:47012)

[BCPRSW]
M.-T. Benameur, A.L. Carey, J. Phillips, A. Rennie, F.A. Sukochev and K.P. Wojciechowski, ``An analytic approach to spectral flow in von Neumann algebras'', Analysis, Geometry and Topology of Elliptic Operators. Papers in Honor of Krzysztof P. Wojciechowski, World Sci. Publ., Singapore, 2006, pp. 297-352. MR 2246773

[BLP]
B. Booss-Bavnbek, M. Lesch and J. Phillips, ``Unbounded Fredholm operators and spectral flow'', Canad. J. Math. 57 (2005), no. 2, pp. 225-250. MR 2124916 (2006a:58029)

[CP1]
A. Carey and J. Phillips, ``Unbounded Fredholm modules and spectral flow'', Canad. J. Math. 50 (1998), no. 4, pp. 673-718. MR 1638603 (2000g:58041)

[CP2]
A. Carey and J. Phillips, ``Spectral flow in Fredholm modules, eta invariants and the JLO cocycle'', $ K$-Theory 31 (2004), no. 2, pp. 135-194. MR 2053481 (2005f:58043)

[Gl]
E. Getzler, ``The odd Chern character in cyclic homology and spectral flow'', Topology 32 (1993), no. 3, pp. 489-507. MR 1231957 (95c:46118)

[GS]
E. Getzler and A. Szenes, ``On the Chern character of a theta-summable Fredholm module'', J. Funct. Anal. 84 (1989), no. 2, pp. 343-357. MR 1001465 (91g:19007)

[KL]
P. Kirk and M. Lesch, ``The $ \eta$-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary'', Forum Math. 16 (2004), no. 4, pp. 553-629. MR 2044028 (2005b:58029)

[L]
M. Lesch, ``The uniqueness of the spectral flow on spaces of unbounded self-adjoint Fredholm operators'', Contemp. Math. 366 (2005), pp. 193-224. MR 2114489 (2005m:58049)

[Wa]
C. Wahl, ``A new topology on the space of unbounded selfadjoint operators and the spectral flow'', preprint math.FA/0607783 on arXiv (2006).

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 58J30, 47B10

Retrieve articles in all Journals with MSC (2000): 58J30, 47B10

Additional Information:

Charlotte Wahl
Affiliation: Mathematisches Inst., Georg-August-Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany
Email: ac.wahl@web.de

DOI: 10.1090/S0002-9939-07-08919-8
PII: S 0002-9939(07)08919-8
Keywords: Spectral flow, integral formula, winding number, Schatten ideal
Received by editor(s): July 5, 2006, and in revised form, September 11, 2006
Posted: September 12, 2007
Communicated by: Mikhail Shubin
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia