The Michigan Mathematical Journal

L 2-Betti numbers of plane algebraic curves

Stefan Friedl, Constance Leidy, and Laurentiu Maxim

Source: Michigan Math. J. Volume 58, Issue 2 (2009), 411-421.

Primary Subjects: 14H30
Secondary Subjects: 57M27

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Permanent link to this document: http://projecteuclid.org/euclid.mmj/1250169069
Digital Object Identifier: doi:10.1307/mmj/1250169069

References

R. G. Burns and V. W. Hale, A note on group rings of certain torsion-free groups, Canad. Math. Bull. 15 (1972), 441--445.
Mathematical Reviews (MathSciNet): MR310046
T. Cochran, Noncommutative knot theory, Algebr. Geom. Topol. 4 (2004), 347--398.
Mathematical Reviews (MathSciNet): MR2077670
T. Cochran, K. Orr, and P. Teichner, Knot concordance, Whitney towers and $L^2$-signatures, Ann. of Math. (2) 157 (2003), 433--519.
Mathematical Reviews (MathSciNet): MR1973052
Zentralblatt MATH: 1044.57001
Digital Object Identifier: doi:10.4007/annals.2003.157.433
J. I. Cogolludo and V. Florens, Twisted Alexander polynomials of plane algebraic curves, J. London Math. Soc. (2) 76 (2007), 105--121.
Mathematical Reviews (MathSciNet): MR2351611
Zentralblatt MATH: 1151.14022
Digital Object Identifier: doi:10.1112/jlms/jdm004
M. W. Davis, T. Januszkiewicz, and I. J. Leary, The $l^2$-cohomology of hyperplane complements, Groups, Geom. Dyn. 1 (2007), 301--309.
Mathematical Reviews (MathSciNet): MR2314047
Zentralblatt MATH: 1148.52012
A. Dimca, Singularities and topology of hypersurfaces, Universitext, Springer-Verlag, New York, 1992.
Mathematical Reviews (MathSciNet): MR1194180
Zentralblatt MATH: 0753.57001
A. Dimca and L. Maxim, Multivariable Alexander invariants of hypersurface complements, Trans. Amer. Math. Soc. 359 (2007), 3505--3528.
Mathematical Reviews (MathSciNet): MR2299465
Zentralblatt MATH: 1119.32012
Digital Object Identifier: doi:10.1090/S0002-9947-07-04241-9
J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates, Approximating $L^2$-invariants, and the Atiyah conjecture, Comm. Pure Appl. Math. 56 (2003), 839--873.
Mathematical Reviews (MathSciNet): MR1990479
Zentralblatt MATH: 1036.58017
Digital Object Identifier: doi:10.1002/cpa.10076
S. Harvey, Higher-order polynomial invariants of 3-manifolds giving lower bounds for the Thurston norm, Topology 44 (2005), 895--945.
Mathematical Reviews (MathSciNet): MR2153977
Digital Object Identifier: doi:10.1016/j.top.2005.03.001
------, Homology cobordism invariants and the Cochran--Orr--Teichner filtration of the link concordance group, Geom. Topol. 12 (2008), 387--430.
Mathematical Reviews (MathSciNet): MR2390349
C. Leidy and L. Maxim, Higher-order Alexander invariants of plane algebraic curves, Internat. Math. Res. Notices 2006 (2006), article ID 12976.
Mathematical Reviews (MathSciNet): MR2264729
Zentralblatt MATH: 1135.14018
------, Obstructions on fundamental groups of plane curve complements, Proceedings of the IX workshop on real and complex singularities (Sao Carlos, 2006) (to appear).
A. Libgober, Alexander polynomial of plane algebraic curves and cyclic multiple planes, Duke Math. J. 49 (1982), 833--851.
Mathematical Reviews (MathSciNet): MR683005
Zentralblatt MATH: 0524.14026
Digital Object Identifier: doi:10.1215/S0012-7094-82-04941-9
Project Euclid: euclid.dmj/1077315533
------, Alexander invariants of plane algebraic curves, Singularities, part 2 (Arcata, 1981), Proc. Sympos. Pure Math., 40, pp. 135--143, Amer. Math. Soc., Providence, RI, 1983.
Mathematical Reviews (MathSciNet): MR713242
Zentralblatt MATH: 0536.14009
------, On the homotopy type of the complement to plane algebraic curves, J. Reine Angew. Math. 367 (1986), 103--114.
Mathematical Reviews (MathSciNet): MR839126
------, On the homology of finite abelian covers, Topology Appl. 43 (1992), 157--166.
Mathematical Reviews (MathSciNet): MR1152316
Zentralblatt MATH: 0770.14004
Digital Object Identifier: doi:10.1016/0166-8641(92)90137-O
------, Homotopy groups of the complements to singular hypersurfaces, II, Ann. of Math. (2) 139 (1994), 117--144.
Mathematical Reviews (MathSciNet): MR1259366
Zentralblatt MATH: 0815.57017
Digital Object Identifier: doi:10.2307/2946629
------, Characteristic varieties of algebraic curves, Applications of algebraic geometry to coding theory, physics and computation (Eilat, 2001), NATO Sci. Ser. II Math. Phys. Chem., 36, pp. 215--254, Kluwer, Dordrecht, 2001.
Mathematical Reviews (MathSciNet): MR1866902
Zentralblatt MATH: 1045.14016
P. Linnell, Zero divisors and $L^2(G),$ C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), 49--53.
Mathematical Reviews (MathSciNet): MR1172405
W. Lück, $L^2$-invariants: Theory and applications to geometry and $K$-theory, Ergeb. Math. Grenzgeb. (3), 44, Springer-Verlag, Berlin, 2002.
Mathematical Reviews (MathSciNet): MR1926649
L. Maxim, Intersection homology and Alexander modules of hypersurface complements, Comment. Math. Helv. 81 (2006), 123--155.
Mathematical Reviews (MathSciNet): MR2208801
J. Milnor, Morse theory, Ann. of Math. Stud., 51, Princeton Univ. Press, Princeton, NJ, 1963.
------, Singular points of complex hypersurfaces, Ann. of Math. Stud., 61, Princeton Univ. Press, Princeton, NJ, 1968.
Mathematical Reviews (MathSciNet): MR239612
H. Reich, Group von Neumann algebras and related algebras, Thesis, Univ. of Göttingen, 1998.

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