Homotopy invariance of twisted higher signatures on manifolds with boundary

éric Leichtnam; Paolo Piazza

Bulletin de la Société Mathématique de France (1999)

  • Volume: 127, Issue: 2, page 307-331
  • ISSN: 0037-9484

How to cite

top

Leichtnam, éric, and Piazza, Paolo. "Homotopy invariance of twisted higher signatures on manifolds with boundary." Bulletin de la Société Mathématique de France 127.2 (1999): 307-331. <http://eudml.org/doc/87808>.

@article{Leichtnam1999,
author = {Leichtnam, éric, Piazza, Paolo},
journal = {Bulletin de la Société Mathématique de France},
keywords = {homotopy invariants; higher signatures; signature operator; L-class; universal cover; Atiyah-Patodi-Singer higher index theory; higher eta invariants; b-pseudodifferential calculus},
language = {eng},
number = {2},
pages = {307-331},
publisher = {Société mathématique de France},
title = {Homotopy invariance of twisted higher signatures on manifolds with boundary},
url = {http://eudml.org/doc/87808},
volume = {127},
year = {1999},
}

TY - JOUR
AU - Leichtnam, éric
AU - Piazza, Paolo
TI - Homotopy invariance of twisted higher signatures on manifolds with boundary
JO - Bulletin de la Société Mathématique de France
PY - 1999
PB - Société mathématique de France
VL - 127
IS - 2
SP - 307
EP - 331
LA - eng
KW - homotopy invariants; higher signatures; signature operator; L-class; universal cover; Atiyah-Patodi-Singer higher index theory; higher eta invariants; b-pseudodifferential calculus
UR - http://eudml.org/doc/87808
ER -

References

top
  1. [APS1] ATIYAH (M.F.), PATODI (V.), SINGER (I.). — Spectral Asymmetry and Riemannian Geometry, I, Math. Proc. Cambridge Phil. Soc., t. 77, p. 43, 1975. Zbl0297.58008MR53 #1655a
  2. [APS2] ATIYAH (M.F.), PATODI (V.), SINGER (I.). — Spectral Asymmetry and Riemannian Geometry, I, Math. Proc. Cambridge Phil. Soc., t. 78, p. 405, 1976. Zbl0314.58016
  3. [AS] ATIYAH (M.F.), SINGER (I.). — The index of elliptic operators, III, Ann. Math., t. 87, 1968, p. 546. Zbl0164.24301
  4. [BiCh] BISMUT (J.-M.), CHEEGER (J.). — Remarks on The Index Theorem for Families of Dirac Operators on Manifolds with Boundary. — Differential Geometricy, B. Lawson and K. Teneblat (eds), Longman Scientific, 1992. 
  5. [Ch1] CHEEGER (J.). — On the Hodge Theory of Riemannian Pseudomanifolds, Proc. Symposia Pure Mathematics, vol. 36, p. 91, 1980. Zbl0461.58002MR83a:58081
  6. [Ch2] CHEEGER (J.). — Spectral Geometry of Singular Riemann Spaces, J. Diff. Geom., t. 18, 1983, p. 575. Zbl0529.58034MR85d:58083
  7. [Co] CONNES (A.). — Noncommutative geometry. — Academic Press, 1994. Zbl0818.46076MR95j:46063
  8. [CM] CONNES (A.), MOSCOVICI (H.). — Cyclic Cohomology, the Novikov Conjecture and Hyperbolic Groups, Topology, t. 29, 1990, p. 345. Zbl0759.58047MR92a:58137
  9. [FS] FINTUSHEL (R.), STERN (R.). — Rational blowdowns of smooth 4-manifolds, J. Diff. Geom., t. 46, 1997, p. 181. Zbl0896.57022MR98j:57047
  10. [FRR] FERRY (S.), RANICKI (A.), ROSENBERG (J.). — A history and survey of the Novikov conjecture, in Novikov Conjectures, Index Theorems and Rigidity, vol. 1, London Math. Soc., Lecture Notes Series, t. 226, 1995. Zbl0954.57018MR97f:57036
  11. [Ka] KAROUBI (M.). — Homologie Cyclique et K-Théorie, Astérisque, t. 149, 1987. Zbl0648.18008MR89c:18019
  12. [HS] HILSUM (M.), SKANDALIS (G.). — Invariance par homotopie de la signature à coefficient dans un fibré presque plat, J. reine angew. Math., t. 423, 1992, p. 73. Zbl0731.55013MR93b:46137
  13. [LP1] LEICHTNAM (E.), PIAZZA (P.). — The b-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem, Mémoires Soc. Math. France, t. 68, 1997. Zbl0942.58003MR99d:58168
  14. [LP2] LEICHTNAM (E.), PIAZZA (P.). — Spectral sections and higher Atiyah-Patodi-Singer index theory on Galois coverings, GAFA, t. 8, 1996, p. 17. Zbl0913.58055MR2000b:58043
  15. [LP3] LEICHTNAM (E.), PIAZZA (P.). — Higher eta invariants and the Novikov conjecture on manifolds with boundary, C. R. Acad. Sciences, t. 327 serie I, 1998, p. 497-502. Zbl0920.58046MR99j:58199
  16. [L1] LOTT (J.). — Superconnections and higher index theory, GAFA, t. 2, 1992, p. 421. Zbl0777.58038MR93j:58128
  17. [L2] LOTT (J.). — Higher eta invariants, K-Theory, t. 6, 1992, p. 191. Zbl0773.58026MR93j:58129
  18. [L3] LOTT (J.). Diffeomorphisms, Analytic Torsion and Non Commutative Geometry, Memoires AMS (in press), circulating as Preprint Max Planck Institute, Bonn, 1996. 
  19. [L4] LOTT (J.). — The Zero-in-the-Spectrum Question, Enseign. Math., t. 42, 1996, p. 341-376. Zbl0874.58086MR97h:58145
  20. [Lu] LUSZTIG (G.). — Novikov's Higher Signature and Families of Elliptic Operators, J. Differential. Geom., t. 7, 1971, p. 229. Zbl0265.57009MR48 #1250
  21. [Me] MELROSE (R.). — The Atiyah-Patodi-Singer Index Theorem. — A. and K. Peters, 1993. Zbl0796.58050MR96g:58180
  22. [MP1] MELROSE (R.), PIAZZA (P.). — Families of Dirac operators, boundaries and the b-calculus, J. Differential. Geom., t. 46, n° 1, 1997, p. 99. Zbl0955.58020MR99a:58144
  23. [MP2] MELROSE (R.), PIAZZA (P.). — An index theorem for families of Dirac operators on odd dimensional manifolds with boundary, J. Differential. Geom., t. 46, n° 2, 1997, p. 287. Zbl0920.58053MR99a:58145
  24. [Pi] PIAZZA (P.). — Dirac operators, heat kernels and microlocal analysis, Part I, Rend. Circolo Mat. Palermo, t. 49, 1997, p. 187. Zbl0906.58050

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.