By Matthias Lesch, Bernhelm Booss-Bavnbek, Slawomir Klimek, Weiping Zhang
Sleek thought of elliptic operators, or just elliptic idea, has been formed through the Atiyah-Singer Index Theorem created forty years in the past. Reviewing elliptic conception over a extensive variety, 32 best scientists from 14 various international locations current fresh advancements in topology; warmth kernel concepts; spectral invariants and slicing and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. the 1st of its variety, this quantity is perfect to graduate scholars and researchers attracted to cautious expositions of newly-evolved achievements and views in elliptic concept. The contributions are in keeping with lectures offered at a workshop acknowledging Krzysztof P Wojciechowski's paintings within the concept of elliptic operators.
Read Online or Download Analysis, Geometry And Topology of Elliptic Operators: Papers in Honor of Krysztof P. Wojciechowski PDF
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Extra info for Analysis, Geometry And Topology of Elliptic Operators: Papers in Honor of Krysztof P. Wojciechowski
78 (1975), 405432. 3. , Spectral asymmetry and Riemannian geometry III, Math. Proc. Cambridge Philos. Soc. 79 (1976), 71-99. 4. B. Boofl and K. P. Wojciechowski, Desuspension and splitting elliptic symbols I, Ann. Global Anal. Geom. 3 (1985), 337-383. 5. , Desuspension and splitting elliptic symbols II, Ann. Global Anal. Geom. 4 (1986), 349-400. 6. B. Boofi-Bavnbek, M. Lesch, and C. Zhu, In preparation. Aspects of the mathematical work of Krzysztof P. Wojciechowski 21 7. B. BooC-Bavnbek and K. P.
P. Loya and J. Park, Decomposition of the zeta-determinant for the Laplacian on manifolds with cylindrical end, Illinois J. Math. 48, no. 4 (2004), 1279-1303. 17. P. Loya and J. Park, On the gluing problem for the spectral invariants of Dirac operators, Adv. , to appear. 18. P. Loya and J. Park, On the gluing problem for Dirac operators on manifolds with cylindrical ends, J. Geom. Anal. 15 (2005), 285-319. 19. P. Loya and J. Park, The comparison problem for the spectral invariants of Dirac type operators, Preprint, 2004.
Recall that A can be regarded as an equivalence class of bundle maps VQ —• V\ for complex vector bundles VQ and V\ over T*X. ),) I be a compact 48 David Bleecker subset of T*X. , see ,  and ) that we can represent any A G K(T*X) by some p G F,\lm(E,F) for some complex vector bundles E and F over X, where p(£) is an isomorphism for |£| > c > 0 and m G R can be chosen arbitrarily. The analytic index of A G K(T*X) is defined by index a (A) := index(Op(p)). Of course one needs to check that index(Op(p)) is independent of the choice of m and p G El\m(E,F) representing A.