## Algebraic & Geometric Topology

### About the macroscopic dimension of certain PSC–Manifolds

Dmitry Bolotov

#### Abstract

In this note we give a partial answer to Gromov’s question about macroscopic dimension filling of a closed spin PSC–Manifold’s universal covering.

#### Article information

Source
Algebr. Geom. Topol., Volume 9, Number 1 (2009), 21-27.

Dates
Revised: 8 December 2008
Accepted: 10 December 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796956

Digital Object Identifier
doi:10.2140/agt.2009.9.21

Mathematical Reviews number (MathSciNet)
MR2471130

Zentralblatt MATH identifier
1185.57026

Subjects
Primary: 57R19: Algebraic topology on manifolds
Secondary: 57R20: Characteristic classes and numbers

#### Citation

Bolotov, Dmitry. About the macroscopic dimension of certain PSC–Manifolds. Algebr. Geom. Topol. 9 (2009), no. 1, 21--27. doi:10.2140/agt.2009.9.21. https://projecteuclid.org/euclid.agt/1513796956

#### References

• D V Bolotov, Macroscopic dimension of 3–manifolds, Math. Phys. Anal. Geom. 6 (2003) 291–299
• D V Bolotov, Gromov's macroscopic dimension conjecture, Algebr. Geom. Topol. 6 (2006) 1669–1676
• M Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures, from: “Functional analysis on the eve of the 21st century, Vol. II (New Brunswick, NJ, 1993)”, Progr. Math. 132, Birkhäuser, Boston (1996) 1–213
• M Gromov, H B Lawson, Positive curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. I.H.E.S 58 (1983) 295–408
• N Hitchin, Harmonic spinors, Advances in Math. 14 (1974) 1–55
• J Rosenberg, $C^*$–algebras, positive scalar curvature, and the Novikov conjecture. III, Topology 25 (1986) 319–336