Algebraic & Geometric Topology Volume 10, issue 2 (2010)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

Lusternik–Schnirelmann category, complements of skeleta and a theorem of Dranishnikov

John Oprea and Jeff Strom

Algebraic & Geometric Topology 10 (2010) 1165–1186

DOI: 10.2140/agt.2010.10.1165

Bibliography

1	P S Alexandrov, Combinatorial topology. Vol. 1, 2 and 3, Dover Publications (1998) 650 MR1643155
2	C Allday, J Oprea, A c-symplectic free $S^1$–manifold with contractible orbits and $\mathrm{cat}=\frac12$ DIM, Proc. Amer. Math. Soc. 134 (2006) 599 MR2176029
3	I Berstein, On the Lusternik–Schnirelmann category of Grassmannians, Math. Proc. Cambridge Philos. Soc. 79 (1976) 129 MR0400212
4	M Clapp, D Puppe, Invariants of the Lusternik–Schnirelmann type and the topology of critical sets, Trans. Amer. Math. Soc. 298 (1986) 603 MR860382
5	O Cornea, G Lupton, J Oprea, D Tanré, Lusternik–Schnirelmann category, Math. Surveys and Monogr. 103, Amer. Math. Soc. (2003) MR1990857
6	A N Dranishnikov, On the Lusternik–Schnirelmann category of spaces with $2$–dimensional fundamental group, Proc. Amer. Math. Soc. 137 (2009) 1489 MR2465675
7	A N Dranishnikov, The Lusternik–Schnirelmann category and the fundamental group, Algebr. Geom. Topol. 10 (2010) 917
8	A N Dranishnikov, M G Katz, Y B Rudyak, Small values of the Lusternik–Schnirelmann category for manifolds, Geom. Topol. 12 (2008) 1711 MR2421138
9	A N Dranishnikov, Y B Rudyak, On the Berstein–Svarc theorem in dimension 2, Math. Proc. Cambridge Philos. Soc. 146 (2009) 407 MR2475974
10	J C Gómez-Larrañaga, F González-Acuña, Lusternik–Schnirelmann category of $3$–manifolds, Topology 31 (1992) 791 MR1191380
11	R E Gompf, A new construction of symplectic manifolds, Ann. of Math. $(2)$ 142 (1995) 527 MR1356781
12	D P Grossman, An estimation of the category of Lusternik–Shnirelman, C. R. $($Doklady$)$ Acad. Sci. URSS $($N.S.$)$ 54 (1946) 109 MR0018820
13	J A Hillman, $\mathrm{PD}_4$–complexes with free fundamental group, Hiroshima Math. J. 34 (2004) 295 MR2120518
14	R Ibáñez, J Kȩdra, Y Rudyak, A Tralle, On fundamental groups of symplectically aspherical manifolds, Math. Z. 248 (2004) 805 MR2103543
15	A Lundell, S Weingram, The topology of CW complexes, Univ. Ser. Higher Math. VIII, Van Nostrand Reinhold (1969)
16	T Matumoto, A Katanaga, On $4$–dimensional closed manifolds with free fundamental groups, Hiroshima Math. J. 25 (1995) 367 MR1336904
17	R Nendorf, N Scoville, J Strom, Categorical sequences, Algebr. Geom. Topol. 6 (2006) 809 MR2240916
18	J Oprea, Category bounds for nonnegative Ricci curvature manifolds with infinite fundamental group, Proc. Amer. Math. Soc. 130 (2002) 833 MR1866039
19	J Oprea, Y Rudyak, Detecting elements and Lusternik–Schnirelmann category of $3$–manifolds, from: "Lusternik–Schnirelmann category and related topics (South Hadley, MA, 2001)" (editors O Cornea, G Lupton, J Oprea, D Tanré), Contemp. Math. 316, Amer. Math. Soc. (2002) 181 MR1962163
20	P A Ostrand, Dimension of metric spaces and Hilbert's problem $13$, Bull. Amer. Math. Soc. 71 (1965) 619 MR0177391
21	F Roth, On the category of Euclidean configuration spaces and associated fibrations, from: "Groups, homotopy and configuration spaces" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13, Geom. Topol. Publ. (2008) 447 MR2508218
22	Y B Rudyak, J Oprea, On the Lusternik–Schnirelmann category of symplectic manifolds and the Arnold conjecture, Math. Z. 230 (1999) 673 MR1686579
23	H Seifert, W Threlfall, Seifert and Threlfall: a textbook of topology, Pure and Applied Math. 89, Academic Press (1980) MR575168
24	B Strom, Personal communication (2008)
25	J Strom, Lusternik–Schnirelmann category of spaces with free fundamental group, Algebr. Geom. Topol. 7 (2007) 1805 MR2366179
26	A S Švarc, The genus of a fibered space, Trudy Moskov. Mat. Obšč. 10 (1961) 217 MR0154284