Geodesic
On macroscopic dimension of universal coverings of closed manifolds
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 2, pp. 279-296.

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We give a homological characterization of $n$-manifolds whose universal covering $\widetilde{M}$ has Gromov’s macroscopic dimension $\mathrm{dim}_{mc}\widetilde{M}$. As the result we distinguish $\mathrm{dim}_{mc}$ from the macroscopic dimension $\mathrm{dim}_{MC}$ defined by the author [7]. We prove the inequality $\mathrm{dim}_{mc}\widetilde{M}\mathrm{dim}_{MC}\widetilde{M}=n$ for every closed $n$-manifold $M$ whose fundamental group $\pi$ is a geometrically finite amenable duality group with the cohomological dimension $cd(\pi)>n$. References: 14 entries. 
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A. Dranishnikov. On macroscopic dimension of universal coverings of closed manifolds. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 2, pp. 279-296. http://geodesic.mathdoc.fr/item/MMO_2013_74_2_a4/

[1] Bell G., Dranishnikov A., “A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory”, Trans. AMS, 358:11 (2006), 4749–4764 | DOI | MR | Zbl

[2] Berstein I., “On the Lusternik–Schnirelmann category of Grassmannians”, Math. Proc. Camb. Philos. Soc., 79 (1976), 129–134 | DOI | MR | Zbl

[3] Bolotov D., “Macroscopic dimension of 3-Manifolds”, Math. Physics, Analysis and Geometry, 6 (2003), 291–299 | DOI | MR | Zbl

[4] Brown K., Cohomology of groups, Springer, 1982 | MR | Zbl

[5] Brunnbauer M., Hanke B., “Large and small group homology”, J. Topol., 3:2 (2010), 463–486 | DOI | MR | Zbl

[6] Bolotov D., Dranishnikov A., “On Gromov's scalar curvature conjecture”, Proc. AMS, 138:4 (2010), 1517–1524 | DOI | MR | Zbl

[7] Dranishnikov A., “On macroscopic dimension of rationally essential manifolds”, Geom. Topol., 15:2 (2011), 1107–1124 | DOI | MR | Zbl

[8] Dranishnikov A. N., “Macroscopic dimension and essential manifolds”, Sovremennye problemy matematiki, Sbornik statei, Trudy MIAN, 273, MAIK, M., 2011, 41–53 | MR

[9] Dranishnikov A., Rudyak Yu., “On the Berstein–Svarc theorem in dimension 2”, Math. Proc. Cambridge Philos. Soc., 146:2 (2009), 407–413 | DOI | MR | Zbl

[10] Gersten S. M., “Cohomological lower bounds for isoperimetric functions on groups”, Topology, 37:5 (1998), 1031–1072 | DOI | MR | Zbl

[11] Gromov M., “Positive curvature, macroscopic dimension, spectral gaps and higher signatures”, Functional analysis on the eve of the 21$^{\mathrm st}$ century, v. II, Birhauser, Boston, MA, 1996 | MR

[12] Gromov M., “Asymptotic invariants of infinite groups”, Geometric Group Theory, v. 2, London Math. Soc. Lecture Note Ser., 182, Cambridge University Press, 1993, 1–295 | MR

[13] Roe J., Lectures on coarse geometry, University Lecture Series, 31, AMS, Providence, RI, 2003 | MR | Zbl

[14] Shvarts A. S., “Rod rassloennogo prostranstva”, Tr. MMO, 10, 1961, 217–272 | MR