Metrics with Positive Scalar Curvature at Infinity and Localization Algebra

Xiaofei Zhang , Yanlin Liu , Hongzhi Liu

Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (2) : 173 -198.

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Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (2) : 173 -198. DOI: 10.1007/s11401-021-0252-y
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Metrics with Positive Scalar Curvature at Infinity and Localization Algebra

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Abstract

In this paper, the authors give a new proof of Block and Weinberger’s Bochner vanishing theorem built on direct computations in the K-theory of the localization algebra.

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Positive scalar curvature at infinity / K-theory of C*-algebras / Higher index theory

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Xiaofei Zhang, Yanlin Liu, Hongzhi Liu. Metrics with Positive Scalar Curvature at Infinity and Localization Algebra. Chinese Annals of Mathematics, Series B, 2021, 42(2): 173-198 DOI:10.1007/s11401-021-0252-y

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References

[1]

Atiyah M F, Singer I M. The index of elliptic operators on compact manifolds. Bull. Amer. Math. Soc., 1963, 69: 422-433

[2]

Block J, Weinberger S. Arithmetic manifolds of positive scalar curvature. J. Differential Geom., 1999, 52(2): 375-406

[3]

Gromov M, Lawson H B Jr. Spin and scalar curvature in the presence of a fundamental group I. Ann. of Math. (2), 1980, 111(2): 209-230

[4]

Gromov M, Lawson H B Jr. Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Inst. Hautes Études Sci. Publ. Math., 1983, 58(1984): 83-196

[5]

Higson N, Roe J. Analytic K-Homology, 2000, Oxford: Oxford University Press

[6]

Hirsch M W. Differential Topology, Graduate Texts in Mathematics, 1994, New York: Springer-Verlag 33

[7]

Kasparov G G. Topological invariants of elliptic operators, I, K-homology. Izv. Akad. Nauk SSSR Ser. Mat., 1975, 39(4): 796-838

[8]

Lawson H B Jr. Michelsohn M-L. Spin Geometry, 1989, Princeton, NJ: Princeton University Press

[9]

Lichnerowicz A. Spineurs harmoniques. C. R. Acad. Sci. Paris, 1963, 257: 7-9

[10]

Roe J. Coarse cohomology and index theory on complete riemannian manifolds. Memoirs of the American Mathematical Society, 1993, 104(497): 1-90

[11]

Roe J. Positive curvature, partial vanishing theorems and coarse indices. Proc. Edinb. Math. Soc. (2), 2016, 59(1): 223-233

[12]

Spivak M. A Comprehensive Introduction to Differential Geometry, 1970, Waltham, Mass.: Published by M. Spivak, Brandeis Univ.

[13]

Wegge-Olsen N E. K-theory and C*-algebras, Oxford Science Publications, 1993, New York: The Clarendon Press, Oxford University Press

[14]

Willett, R. and Yu, G., Higher Index Theory, Book draft. http://math.hawaii.edu/rufus/higherindextheory, 2019

[15]

Xie Z, Yu G. A relative higher index theorem, diffeomorphisms and positive scalar curvature. Adv. Math., 2014, 250: 35-73

[16]

Xie Z, Yu G. Positive scalar curvature, higher rho invariants and localization algebras. Adv. Math., 2014, 262: 823-866

[17]

Yu G. Localization algebras and the coarse Baum-Connes conjecture. K-Theory, 1997, 11(4): 307-318

[18]

Yu G. The Novikov conjecture for groups with finite asymptotic dimension. Ann. of Math. (2), 1998, 147(2): 325-355

[19]

Yu G. A characterization of the image of the Baum-Connes map, Quanta of Maths. Clay Math. Proc., 2010, Providence, RI: Amer. Math. Soc. 649-657 Vol. 11

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