Positive scalar curvature and odd order

abelian fundamental groups

Author:
Reinhard Schultz

Journal:
Proc. Amer. Math. Soc. **125** (1997), 907-915

MSC (1991):
Primary 53C21, 55N15, 57R75; Secondary 53C20, 57R85

DOI:
https://doi.org/10.1090/S0002-9939-97-03683-6

MathSciNet review:
1363184

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Abstract | References | Similar Articles | Additional Information

Abstract: If a smooth manifold has a Riemannian metric with positive scalar curvature, it follows immediately that the universal covering also has such a metric. The paper establishes a converse if the manifold in question is closed of dimension at least 5 and the fundamental group is an elementary abelian -group of rank 2, where is an odd prime.

**[A]**M. Atiyah,*-theory*(notes by D. W. Anderson), Addison-Wesley, Reading, Mass., 1989. MR**90m:18011****[B]**N. Baas,*On the bordism theory of manifolds with singularities*, Math. Scand.**33**(1973), 279-302. MR**49:11547b****[BeS]**J. C. Becker and R. E. Schultz,*Equivariant function spaces and stable homotopy theory*, Comment. Math. Helv.**49**(1974), 1-34. MR**49:3994****[Ho]**R. Holzsager,*Stable splitting of*, Proc. Amer. Math. Soc.**31**(1972), 305-306. MR**44:4744****[Hn]**T. Hungerford,*Multiple Künneth formulas for abelian groups*, Trans. Amer. Math. Soc.**118**(1965), 257-275. MR**31:229****[J]**R. Jung, Ph. D. Thesis, Univ. Mainz, in preparation.**[KS1]**S. Kwasik and R. Schultz,*Positive scalar curvature and periodic fundamental groups*, Comment. Math. Helv.**65**(1990), 271-286. MR**91k:57027****[KS2]**-,*Fake spherical spaceforms with constant positive scalar curvature*, Comment. Math. Helv.**71**(1996), 1-40. CMP**96:07****[L1]**P. Landweber,*Künneth formulas for bordism theories*, Trans. Amer. Math. Soc.**121**(1966), 242-256. MR**33:728****[L2]**-,*Complex bordism of classifying spaces*, Proc. Amer. Math. Soc.**27**(1971), 175-179. MR**42:3782****[MP]**S. Mitchell and S. Priddy,*Stable splittings derived from the Steinberg module*, Topology**22**(1983), 285-298. MR**85f:55005****[Rs1]**J. Rosenberg,*-algebras, positive scalar curvature, and the Novikov Conjecture*, Publ. Math. I. H. E. S.**58**(1983), 197-212. MR**85g:58083****[Rs2]**-,*-algebras, positive scalar curvature, and the Novikov Conjecture*-II, Geometric Methods in Operator Algebras (Kyoto, 1983), Pitman Res. Notes Math. Ser. 123, Longman Sci. Tech., Harlow, U. K., pp.341-374. MR**88f:58140****[Rs3]**-,*-algebras, positive scalar curvature, and the Novikov Conjecture*-III, Topology**25**(1986), 319-336. MR**88f:58141****[RsS]**J. Rosenberg and S. Stolz,*A ``stable'' version of the Gromov-Lawson conjecture*, Contemp. Math., vol. 181, Amer. Math. Soc., Providence, RI, 1995, pp. 405-418. CMP**95:09****[Rw]**R. Rowlett,*Free actions of a -group on two generators*, Indiana Univ. Math. J.**26**(1977), 885-889. MR**56:16656**

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Additional Information

**Reinhard Schultz**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Address at time of publication:
Department of Mathematics, University of California, Riverside, California 92521

Email:
schultz@math.ucr.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03683-6

Received by editor(s):
February 13, 1995

Received by editor(s) in revised form:
September 13, 1995

Communicated by:
Thomas Goodwillie

Article copyright:
© Copyright 1997
American Mathematical Society