Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$\cal L$-classes on pseudomanifolds
with one singular stratum


Author: Shing-Wai Chan
Journal: Proc. Amer. Math. Soc. 125 (1997), 1955-1968
MSC (1991): Primary 19D55; Secondary 58G12
DOI: https://doi.org/10.1090/S0002-9939-97-03386-8
MathSciNet review: 1327001
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the index theorem and Chern character of an admissible pseudomanifold $X^{\dagger }$ with one singular stratum. Under a condition on the link, we give a de Rham type realization of the Goresky-MacPherson-Siegel $\cal L$-classes on $X^{\dagger }$ in terms of curvature forms and eta invariant of the link.


References [Enhancements On Off] (What's this?)

  • [BC] J. M. Bismut, J. Cheeger, Remarks on the Index Theorem for families of Dirac Operators on Manifolds with boundary, in Differential Geometry, A Symposium in honour of Manfredo do Carmo, (B. Lawson, K. Teneblat eds.), Longman Scientific & Technical, 1991, 59-83. MR 93k:58211
  • [BGV] N. Berline, E. Getzler, M. Vergne, Heat Kernels and Dirac Operators, Springer Verlag, 1991. MR 94e:58130
  • [BL] J. Brüning, M. Lesch, Kähler-Hodge Theory for Conformal Complex Cones, Geom. and Func. Analysis 3 No.5 (1993), 439-473. MR 94i:58189
  • [BS] J. Brüning, R. Seeley, An Index Theorem for First Order Regular Singular Operators, Amer. J. Math. 110 (1988), 659-714. MR 89k:58271
  • [BT] R. Bott, L. W. Tu, Differential Forms in Algebraic Topology, Grad. Text in Math. Vol. 82, Springer-Verlag, 1982. MR 83i:57016
  • [C1] J. Cheeger, On the Hodge Theory of Riemannian Pseudomanifolds, AMS. Proc. Symp. Pure Math. Vol. 36 (1980), 91-145. MR 83a:58081
  • [C2] J. Cheeger, Spectral Geometry of Singular Riemannian Spaces, J. Diff. Geom. 18 (1983), 575-657. MR 85d:58083
  • [CM] A. Connes, H. Moscovici, Cyclic cohomology, the Novikov conjecture, and hyperbolic groups, Topology 29 No.3 (1990), 345-388. MR 92a:58137
  • [CST] A. Connes, D. Sullivan, N. Teleman, Local formulas for topological Pontryagin classes, C.R. Acad. Sci. Sér. I Math. 317 (1993), 521-526. MR 94h:58165
  • [G] M. Gaffney, Hilbert Space Methods in the Theory of Harmonics Integrals, AMS. Trans. 78 (1955), 426-444. MR 16:957a
  • [GM] M. Goresky, R. MacPherson, Intersection Homology Theory, Topology 19 (1980), 135-162. MR 82b:57010
  • [H1] M. Hilsum, Signature operator of Lipschitz manifolds and Unbounded Kasparov Modules, in Operator Algebras and their connections with Topology and Ergodic Theory, Springer Lect. Notes in Math. 1132 (1985), 254-288. MR 87d:58133
  • [H2] M. Hilsum, Fonctorialité en K-Théorie bivariante pour les variétés lipschitziziennes, K-Theory 3 (1989), 401-440. MR 91j:19012
  • [L1] M, Lesch, Deficiency Indices for Symmetric Dirac Operators on Manifolds with Conic Singularities, Topology 32 No.3 (1993), 611-623. MR 94e:58133
  • [L2] M. Lesch, On a class of singular differential operators and asymptotic methods, Habilitationsschrift, Univ. of Augsburg, 1993.
  • [MS] J. W. Milnor, J. D. Stasheff, Characteristic Classes. Annals of Math, Studies, 76 (1974). MR 55:13428
  • [MW1] H. Moscovici, F.-B. Wu, Localization of Topological Pontryagin Classes via Finite Propagation Speed, Geom. and Func. Analysis 4 No.1 (1994), 52-92. MR 95c:58169
  • [MW2] H. Moscovici, F.-B. Wu, Pontryagin Forms for manifolds with Framed Singular Strata, Geom. and Func. Analysis 5 No.4 (1995), 702-728. MR 96g:58185
  • [RS] M. Reed, B. Simon, Methods of Modern Mathematical Physics I, Functional Analysis, Academic Press, 1980. MR 85e:46002
  • [Si] P. H. Siegel, Witt spaces: a geometry cycle theory for KO-homology at odd primes, Amer. J. Math. 105 (1983), 1067-1105. MR 85f:57011
  • [St] R. E. Stong, Notes on Cobordism theory, Princeton Math. Notes, Princeton Univ. Press, 1958.
  • [Su] D. Sullivan, Infinitesimal calculations in topology, Publ. Math. IHES 47 (1977), 269-331. MR 58:31119
  • [T] F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators, Vol.1, Plenum, 1980. MR 82i:35173

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 19D55, 58G12

Retrieve articles in all journals with MSC (1991): 19D55, 58G12


Additional Information

Shing-Wai Chan
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
Email: swchan@math.ohio-state.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03386-8
Received by editor(s): January 17, 1995
Received by editor(s) in revised form: March 13, 1995, and January 31, 1996
Communicated by: Peter W. K. Li
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society