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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 4, Pages 707–751 (Mi izv924)  

This article is cited in 19 scientific papers (total in 19 papers)

Asymptotic invariants of smooth manifolds

I. K. Babenko

Abstract: Certain new homotopy invariants of non-simply-connected smooth manifolds are constructed and investigated. Relations are examined between these invariants and some questions of “geometry in the large”.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:1, 1–38

Bibliographic databases:

UDC: 515.1644+514.77
MSC: Primary 53C23; Secondary 15A75, 20F05, 49Q05, 52A40, 53C22, 53C42, 57M10
Received: 16.05.1991
Revised: 23.12.1991

Citation: I. K. Babenko, “Asymptotic invariants of smooth manifolds”, Izv. RAN. Ser. Mat., 56:4 (1992), 707–751; Russian Acad. Sci. Izv. Math., 41:1 (1993), 1–38

Citation in format AMSBIB
\by I.~K.~Babenko
\paper Asymptotic invariants of smooth manifolds
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 4
\pages 707--751
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 1
\pages 1--38

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    This publication is cited in the following articles:
    1. I. K. Babenko, “Asymptotic volumes and simply connected surgeries of smooth manifolds”, Russian Acad. Sci. Izv. Math., 44:2 (1995), 427–430  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. K. Babenko, “Extremal problems of geometry, surgery on manifolds, and problems of group theory”, Izv. Math., 59:2 (1995), 321–332  mathnet  crossref  mathscinet  zmath  isi
    3. I. K. Babenko, “Topological entropy of geodesic flows on simply connected manifolds, and related topics”, Izv. Math., 61:3 (1997), 517–535  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. V. Dontsov, “Systoles on Heisenberg groups with Carnot–Carathéodory metrics”, Sb. Math., 192:3 (2001), 347–374  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Mikhail G. Katz, Yuli B. Rudyak, “Lusternik-Schnirelmann category and systolic category of low-dimensional manifolds”, Comm Pure Appl Math, 59:10 (2006), 1433  crossref  mathscinet  zmath  isi  elib
    6. Mikhail G. Katz, Yuli B. Rudyak, Stéphane Sabourau, “Systoles of 2-complexes, Reeb graph, and Grushko decomposition”, Internat Math Res Notices, 2006 (2006), 1  crossref
    7. Stéphane Sabourau, “Systolic volume of hyperbolic manifolds and connected sums of manifolds”, Geom Dedicata, 127:1 (2007), 7  crossref  mathscinet  isi  elib
    8. T. G. Ceccherini-Silberstein, A. Y. Samet-Vaillant, “Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint”, Journal of Mathematical Sciences (New York), 2008  crossref
    9. Brunnbauer M., “Homological Invariance for Asymptotic Invariants and Systolic Inequalities”, Geom. Funct. Anal., 18:4 (2008), 1087–1117  crossref  mathscinet  zmath  isi
    10. Dranishnikov A.N., Katz M.G., Rudyak Yu.B., “Small Values of the Lusternik-Schnirelman Category for Manifolds”, Geom. Topol., 12 (2008), 1711–1727  crossref  mathscinet  zmath  isi
    11. Pablo Suárez-Serrato, “Minimal entropy and geometric decompositions in dimension four”, Algebr Geom Topol, 9:1 (2009), 365  crossref  mathscinet  zmath  isi
    12. Brunnbauer M. Ishida M. Suarez-Serrato P., “An Essential Relation Between Einstein Metrics, Volume Entropy, and Exotic Smooth Structures”, Math. Res. Lett., 16:2-3 (2009), 503–514  mathscinet  zmath  isi
    13. Bruno Martelli, “Complexity of PL manifolds”, Algebr Geom Topol, 10:2 (2010), 1107  crossref  elib
    14. FRANÇOISE DAL’BO, MARC PEIGNÉ, JEAN-CLAUDE PICAUD, ANDREA SAMBUSETTI, “On the growth of quotients of Kleinian groups”, Ergod Th Dynam Sys, 2010, 1  crossref
    15. Hoil Ryu, “Stable systolic category of the product of spheres”, Algebr. Geom. Topol, 11:2 (2011), 983  crossref
    16. Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak, “Cohomological dimension, self-linking, and systolic geometry”, Isr. J. Math, 184:1 (2011), 437  crossref
    17. Ivan Babenko, Florent Balacheff, “Systolic volume of homology classes”, Algebr. Geom. Topol, 15:2 (2015), 733  crossref
    18. Dranishnikov A.N., “The LS category of the product of lens spaces”, Algebr. Geom. Topol., 15:5 (2015), 2985–3010  crossref  mathscinet  zmath  isi  elib  scopus
    19. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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