Remarks on the L2-cohomology of singular algebraic surfaces

Masayoshi NAGASE

doi:10.2969/jmsj/04110097

Remarks on the L²-cohomology of singular algebraic surfaces

Masayoshi NAGASE

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 1 Pages 97-116

DOI https://doi.org/10.2969/jmsj/04110097

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Published: 1989 Received: March 16, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Borel et al., Intersection Cohomology, Birkhäuser, 1984.
2) I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, 1984.
3) J. Cheeger, On the Hodge theory of Riemannian pseudomanifolds, Proc. Symposia Pure Math., 36, Amer. Math. Soc., Providence, 1980, pp. 91-146.
4) J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Diff. Geom., 18 (1983), 575-657.
5) J. Cheeger, M. Goresky and R. MacPherson, L²-cohomoiogy and intersection homology for singular algebraic varieties, Ann. Math. Studies, 102, Seminar on Differential Geometry, 1982, pp. 303-340.
6) P. E. Conner, The Neumann's problem for differential forms on Riemannian manifolds, Mem. Amer. Math. Soc., 20 (1956).
7) M. Goresky and R. MacPherson, Intersection homology theory, Topology, 19 (1980), 135-162.
8) M. Goresky and R. MacPherson, Intersection homology II, Invent. Math., 72 (1983), 77-130.
9) W. C. Hsiang and V. Pati, L²-cohomology of normal algebraic surfaces I, Invent. Math., 81 (1985), 395-412.
10) H. B. Laufer, Normal Two-dimensional Singularities, Ann. Math. Studies, 71, 1971.
11) M. Nagase, L²-cohomology and intersection homology of stratified spaces, Duke Math. J., 50 (1983), 329-368.
12) M. Nagase, Sheaf theoretic L²-cohmology, Advanced Studies in Pure Math., 8, Complex Analytic Singularities, Kinokuniya and North Holland, 1986, pp. 273-279.
13) M. Nagase, On the heat operators of cuspidally stratified Riemannian spaces, Proc. Japan Acad., 62 (1986), 58-60.
14) M. Nagase, On the heat operators of normal singular algebraic surfaces, J. Diff. Geom., 28 (1988), 37-57.
15) M. Reed and B. Simon, Methods of Modern Mathematical Physics I: Functional Analysis, Academic Press, 1980.
16) E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations I, Oxford, 1946.

Right : [1] A. Borel et al., Intersection Cohomology, Birkhäuser, 1984.
[2] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, 1984.
[3] J. Cheeger, On the Hodge theory of Riemannian pseudomanifolds, Proc. Symposia Pure Math., 36, Amer. Math. Soc., Providence, 1980, pp. 91-146.
[4] J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Diff. Geom., 18 (1983), 575-657.
[5] J. Cheeger, M. Goresky and R. MacPherson, L²-cohomoiogy and intersection homology for singular algebraic varieties, Ann. Math. Studies, 102, Seminar on Differential Geometry, 1982, pp. 303-340.
[6] P. E. Conner, The Neumann's problem for differential forms on Riemannian manifolds, Mem. Amer. Math. Soc., 20 (1956).
[7] M. Goresky and R. MacPherson, Intersection homology theory, Topology, 19 (1980), 135-162.
[8] M. Goresky and R. MacPherson, Intersection homology II, Invent. Math., 72 (1983), 77-130.
[9] W. C. Hsiang and V. Pati, L²-cohomology of normal algebraic surfaces I, Invent. Math., 81 (1985), 395-412.
[10] H. B. Laufer, Normal Two-dimensional Singularities, Ann. Math. Studies, 71, 1971.
[11] M. Nagase, L²-cohomology and intersection homology of stratified spaces, Duke Math. J., 50 (1983), 329-368.
[12] M. Nagase, Sheaf theoretic L²-cohmology, Advanced Studies in Pure Math., 8, Complex Analytic Singularities, Kinokuniya and North Holland, 1986, pp. 273-279.
[13] M. Nagase, On the heat operators of cuspidally stratified Riemannian spaces, Proc. Japan Acad., 62 (1986), 58-60.
[14] M. Nagase, On the heat operators of normal singular algebraic surfaces, J. Diff. Geom., 28 (1988), 37-57.
[15] M. Reed and B. Simon, Methods of Modern Mathematical Physics I: Functional Analysis, Academic Press, 1980.
[16] E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations I, Oxford, 1946.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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