Algebraic & Geometric Topology Volume 19, issue 7 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Other MSP Journals

An upper bound on the LS category in presence of the fundamental group

Alexander Dranishnikov

Algebraic & Geometric Topology 19 (2019) 3601–3614

DOI: 10.2140/agt.2019.19.3601

Bibliography

1	I Berstein, On the Lusternik–Schnirelmann category of Grassmannians, Math. Proc. Cambridge Philos. Soc. 79 (1976) 129 MR400212
2	A Borel, Seminar on transformation groups, 46, Princeton Univ. Press (1960) MR0116341
3	P Bouwknegt, J Evslin, V Mathai, Spherical T–duality, II : An infinity of spherical T–duals for non-principal SU(2)–bundles, J. Geom. Phys. 92 (2015) 46 MR3328056
4	K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
5	O Cornea, G Lupton, J Oprea, D Tanré, Lusternik–Schnirelmann category, 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 Dranishnikov, The Lusternik–Schnirelmann category and the fundamental group, Algebr. Geom. Topol. 10 (2010) 917 MR2629770
8	A N Dranishnikov, The LS category of the product of lens spaces, Algebr. Geom. Topol. 15 (2015) 2983 MR3426700
9	A N Dranishnikov, M G Katz, Y B Rudyak, Cohomological dimension, self-linking, and systolic geometry, Israel J. Math. 184 (2011) 437 MR2823985
10	A Dranishnikov, R Sadykov, On the LS-category and topological complexity of a connected sum, Proc. Amer. Math. Soc. 147 (2019) 2235 MR3937697
11	D P Grossman, An estimation of the category of Lusternik–Shnirelman, C. R. (Doklady) Acad. Sci. URSS 54 (1946) 109 MR0018820
12	N Iwase, M Mimura, T Nishimoto, Lusternik–Schnirelmann category of non-simply connected compact simple Lie groups, Topology Appl. 150 (2005) 111 MR2133672
13	M G Katz, Y B Rudyak, Lusternik–Schnirelmann category and systolic category of low-dimensional manifolds, Comm. Pure Appl. Math. 59 (2006) 1433 MR2248895
14	L Lusternik, L Schnirelmann, Sur le probleme de trois geodesiquesfermees sur les surfaces de genus 0, C. R. Acad. Sci. Paris Sér. I Math. 189 (1929) 269
15	J Oprea, J Strom, Lusternik–Schnirelmann category, complements of skeleta and a theorem of Dranishnikov, Algebr. Geom. Topol. 10 (2010) 1165 MR2653059
16	P A Ostrand, Dimension of metric spaces and Hilbert’s problem 13, Bull. Amer. Math. Soc. 71 (1965) 619 MR177391
17	Y B Rudyak, On analytical applications of stable homotopy (the Arnold conjecture, critical points), Math. Z. 230 (1999) 659 MR1686583
18	J Strom, Lusternik–Schnirelmann category of spaces with free fundamental group, Algebr. Geom. Topol. 7 (2007) 1805 MR2366179
19	G W Whitehead, The homology suspension, from: "Colloque de topologie algébrique", Georges Thone (1957) 89 MR0094794