#### Volume 12, issue 3 (2008)

 1 I K Babenko, Asymptotic invariants of smooth manifolds, Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992) 707 MR1208148 2 V Bangert, M Katz, S Shnider, S Weinberger, $E_7$, Wirtinger inequalities, Cayley $4$–form, and homotopy, to appear in Duke Math. J. arXiv:math.DG/0608006 3 I Berstein, On the Lusternik–Schnirelmann category of Grassmannians, Math. Proc. Cambridge Philos. Soc. 79 (1976) 129 MR0400212 4 I Berstein, T Ganea, The category of a map and of a cohomology class, Fund. Math. 50 (1961/1962) 265 MR0139168 5 G E Bredon, Sheaf theory, Graduate Texts in Math. 170, Springer (1997) MR1481706 6 K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer (1994) MR1324339 7 O Cornea, G Lupton, J Oprea, D Tanré, Lusternik–Schnirelmann category, Math. Surveys and Monographs 103, Amer. Math. Soc. (2003) MR1990857 8 A Dranishnikov, On the Lusternik–Schnirelmann category of spaces with $2$–dimensional fundamental group, to appear in Proc. Amer. Math. Soc. arXiv:0709.4018 9 A Dranishnikov, M Katz, Y Rudyak, Small values of the systolic category of manifolds, preprint (2008) 10 A Dranishnikov, Y Rudyak, On the Berstein–Svarc Theorem in dimension 2, to appear in Math. Proc. Cambridge Phil. Soc. arXiv:0712.2087 11 E Fadell, S Husseini, Category weight and Steenrod operations, Bol. Soc. Mat. Mexicana $(2)$ 37 (1992) 151 MR1317569 12 A I Fet, A connection between the topological properties and the number of extremals on a manifold, Doklady Akad. Nauk SSSR $($N.S.$)$ 88 (1953) 415 MR0054866 13 R H Fox, On the Lusternik–Schnirelmann category, Ann. of Math. $(2)$ 42 (1941) 333 MR0004108 14 J C Gómez-Larrañaga, F González-Acuña, Lusternik–Schnirelmann category of $3$–manifolds, Topology 31 (1992) 791 MR1191380 15 M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984 16 M Gromov, Systoles and intersystolic inequalities, from: "Actes de la Table Ronde de Géométrie Différentielle (Luminy, 1992)", Sémin. Congr. 1, Soc. Math. France (1996) 291 MR1427763 17 M Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progress in Math. 152, Birkhäuser (1999) MR1699320 18 M Gromov, Metric structures for Riemannian and non-Riemannian spaces, Modern Birkhäuser Classics, Birkhäuser (2007) MR2307192 19 K A Hardie, On the category of the double mapping cylinder, Tôhoku Math. J. $(2)$ 25 (1973) 355 MR0370558 20 A Hatcher, Algebraic topology, Cambridge University Press (2002) MR1867354 21 J A Hillman, $\mathrm{PD}_4$–complexes with free fundamental group, Hiroshima Math. J. 34 (2004) 295 MR2120518 22 M Katz, Systolic geometry and topology, Math. Surveys and Monographs 137, Amer. Math. Soc. (2007) MR2292367 23 M Katz, Y Rudyak, Bounding volume by systoles of $3$–manifolds, to appear in J. London. Math. Soc. arXiv:math.DG/0504008 24 M Katz, Y Rudyak, Lusternik–Schnirelmann category and systolic category of low-dimensional manifolds, Comm. Pure Appl. Math. 59 (2006) 1433 MR2248895 25 M Katz, Y Rudyak, S Sabourau, Systoles of $2$–complexes, Reeb graph, and Grushko decomposition, Int. Math. Res. Not. (2006) 30 MR2250017 26 M Katz, S Shnider, Cayley $4$–form comass and triality isomorphisms, to appear Israel J. Math. arXiv:0801.0283 27 T Matumoto, A Katanaga, On $4$–dimensional closed manifolds with free fundamental groups, Hiroshima Math. J. 25 (1995) 367 MR1336904 28 J Oprea, Y Rudyak, Detecting elements and Lusternik–Schnirelmann category of $3$–manifolds, from: "Lusternik–Schnirelmann category and related topics (South Hadley, MA, 2001)", Contemp. Math. 316, Amer. Math. Soc. (2002) 181 MR1962163 29 Y Rudyak, Category weight: new ideas concerning Lusternik–Schnirelmann category, from: "Homotopy and geometry (Warsaw, 1997)", Banach Center Publ. 45, Polish Acad. Sci. (1998) 47 MR1679849 30 Y Rudyak, On category weight and its applications, Topology 38 (1999) 37 MR1644063 31 E H Spanier, Algebraic topology, McGraw-Hill Book Co. (1966) MR0210112 32 J Stallings, Groups of dimension 1 are locally free, Bull. Amer. Math. Soc. 74 (1968) 361 MR0223439 33 J Strom, Category weight and essential category weight, PhD thesis, Univ. of Wisconsin (1997) 34 J Strom, Lusternik–Schnirelmann category of spaces with free fundamental group, Algebr. Geom. Topol. 7 (2007) 1805 MR2366179 35 R G Swan, Groups of cohomological dimension one, J. Algebra 12 (1969) 585 MR0240177 36 A Švarc, The genus of a fiber space, Amer. Math. Soc. Transl. Ser. 2 55 (1966) 49 37 G W Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics 61, Springer (1978) MR516508