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Journal articles on the topic 'Lusternik'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Hovey, Mark. "Lusternik-Schnirelmann cocategory." Illinois Journal of Mathematics 37, no. 2 (1993): 224–39. http://dx.doi.org/10.1215/ijm/1255987145.

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2

Ayala, R., and A. Quintero. "On the Ganea strong category in proper homotopy." Proceedings of the Edinburgh Mathematical Society 41, no. 2 (1998): 247–63. http://dx.doi.org/10.1017/s0013091500019623.

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This paper contains some basic relations between Ganea strong category and Lusternik Schnirelmann category in proper homotopy theory. We focus our interest on the case of category 2 in order to show that ℚn is the unique open n-manifold with proper Lusternik-Schnirelmann category 2 (n ≠ 3).

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3

Fernández-Ternero, Desamparados, Enrique Macías-Virgós, Erica Minuz, and José Antonio Vilches. "Simplicial Lusternik-Schnirelmann category." Publicacions Matemàtiques 63 (January 1, 2019): 265–93. http://dx.doi.org/10.5565/publmat6311909.

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4

Cornea, Octavian. "Lusternik-Schnirelmann-categorical sections." Annales scientifiques de l'École normale supérieure 28, no. 6 (1995): 689–704. http://dx.doi.org/10.24033/asens.1730.

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5

de Groot, J. A. M., and J. Vermeer. "Lusternik, Schnirelman for subspaces." Topology and its Applications 115, no. 3 (2001): 343–54. http://dx.doi.org/10.1016/s0166-8641(00)00076-6.

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6

BORAT, Ayşe, and Tane VERGİLİ. "Digital Lusternik–Schnirelmann category." TURKISH JOURNAL OF MATHEMATICS 42, no. 4 (2018): 1845–52. http://dx.doi.org/10.3906/mat-1801-94.

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7

ZAPATA, CESAR A. IPANAQUE. "CATEGORY AND TOPOLOGICAL COMPLEXITY OF THE CONFIGURATION SPACE." Bulletin of the Australian Mathematical Society 100, no. 3 (2019): 507–17. http://dx.doi.org/10.1017/s0004972719000479.

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The Lusternik–Schnirelmann category cat and topological complexity TC are related homotopy invariants. The topological complexity TC has applications to the robot motion planning problem. We calculate the Lusternik–Schnirelmann category and topological complexity of the ordered configuration space of two distinct points in the product $G\times \mathbb{R}^{n}$ and apply the results to the planar and spatial motion of two rigid bodies in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ respectively.

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8

Viterbo, Claude. "and the Lusternik-Shnirelman category." Duke Mathematical Journal 86, no. 3 (1997): 547–64. http://dx.doi.org/10.1215/s0012-7094-97-08617-8.

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9

Felix, Yves, Steve Halperin, and Jean-Claude Thomas. "Lusternik–Schnirelmann category of skeleta." Topology and its Applications 125, no. 2 (2002): 357–61. http://dx.doi.org/10.1016/s0166-8641(01)00288-7.

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10

Singh, Harpreet. "Lusternik-Schnirelmann category and cobordism." Proceedings of the American Mathematical Society 102, no. 1 (1988): 183. http://dx.doi.org/10.1090/s0002-9939-1988-0915741-1.

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11

James, I. M. "The Lusternik-Schnirelmann theorem reconsidered." Topology and its Applications 44, no. 1-3 (1992): 197–202. http://dx.doi.org/10.1016/0166-8641(92)90094-g.

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12

YOKOI, KATSUYA. "LUSTERNIK–SCHNIRELMANN CATEGORY BASED ON THE DISCRETE CONLEY INDEX THEORY." Glasgow Mathematical Journal 61, no. 03 (2018): 693–704. http://dx.doi.org/10.1017/s0017089518000447.

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13

Montejano, L. "Lusternik-Schnirelmann category: a geometric approach." Banach Center Publications 18, no. 1 (1986): 117–29. http://dx.doi.org/10.4064/-18-1-117-129.

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14

Iwase, Norio. "A∞-method in Lusternik–Schnirelmann category." Topology 41, no. 4 (2002): 695–723. http://dx.doi.org/10.1016/s0040-9383(00)00045-8.

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15

Vandembroucq, Lucile. "Fibrewise suspension and Lusternik–Schnirelmann category." Topology 41, no. 6 (2002): 1239–58. http://dx.doi.org/10.1016/s0040-9383(02)00007-1.

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16

Gatsinzi, J. B. "Lusternik-Schnirelmann category of classifying spaces." Bulletin of the Belgian Mathematical Society - Simon Stevin 8, no. 3 (2001): 405–9. http://dx.doi.org/10.36045/bbms/1102714567.

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17

Cuvilliez, Maxence, Yves Félix, Barry Jessup, and Paul-Eugène Parent. "Rational Lusternik–Schnirelmann category of fibrations." Journal of Pure and Applied Algebra 174, no. 2 (2002): 117–33. http://dx.doi.org/10.1016/s0022-4049(02)00039-7.

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18

Hofer, H. "Lusternik-Schnirelman-theory for Lagrangian intersections." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 5, no. 5 (1988): 465–99. http://dx.doi.org/10.1016/s0294-1449(16)30339-0.

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19

Green, Brian, Mimi Tsuruga, and Nicholas A. Scoville. "Estimating the discrete Lusternik-Schnirelmann category." Topological Methods in Nonlinear Analysis 45, no. 1 (2015): 103. http://dx.doi.org/10.12775/tmna.2015.006.

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20

Aaronson, Seth, and Nicholas A. Scoville. "Lusternik–Schnirelmann category for simplicial complexes." Illinois Journal of Mathematics 57, no. 3 (2013): 743–53. http://dx.doi.org/10.1215/ijm/1415023508.

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21

Iwase, Norio. "Ganea's Conjecture on Lusternik-Schnirelmann Category." Bulletin of the London Mathematical Society 30, no. 6 (1998): 623–34. http://dx.doi.org/10.1112/s0024609398004548.

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22

COLMAN, HELLEN, and ENRIQUE MACIAS-VIRGÓS. "TANGENTIAL LUSTERNIK–SCHNIRELMANN CATEGORY OF FOLIATIONS." Journal of the London Mathematical Society 65, no. 03 (2002): 745–56. http://dx.doi.org/10.1112/s0024610702003113.

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23

Sanjurjo, José M. R. "Lusternik‐Schnirelmann category and Morse decompositions." Mathematika 47, no. 1-2 (2000): 299–305. http://dx.doi.org/10.1112/s0025579300015904.

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24

Gómez-Larrañaga, J. C., and F. González-Acuña. "Lusternik-Schnirelmann category of 3-manifolds." Topology 31, no. 4 (1992): 791–800. http://dx.doi.org/10.1016/0040-9383(92)90009-7.

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25

Cornea, Octavian. "Cone-length and Lusternik-Schnirelmann category." Topology 33, no. 1 (1994): 95–111. http://dx.doi.org/10.1016/0040-9383(94)90037-x.

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26

Weiyue, Ding. "Lusternik-Schnirelmann theory for harmonic maps." Acta Mathematica Sinica 2, no. 2 (1986): 105–22. http://dx.doi.org/10.1007/bf02564873.

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27

Perez, Juan Julian Rivadeneyra. "On cat (X\p)." International Journal of Mathematics and Mathematical Sciences 15, no. 3 (1992): 465–68. http://dx.doi.org/10.1155/s0161171292000620.

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28

Macías-Virgós, Enrique, María José Pereira-sáez, and Daniel Tanré. "Morse Theory and the Lusternik–Schnirelmann Category of Quaternionic Grassmannians." Proceedings of the Edinburgh Mathematical Society 60, no. 2 (2016): 441–49. http://dx.doi.org/10.1017/s0013091516000195.

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29

Sang, Yanbin, Xiaorong Luo, and Yongqing Wang. "The Choquard Equation with Weighted Terms and Sobolev-Hardy Exponent." Journal of Function Spaces 2018 (July 8, 2018): 1–22. http://dx.doi.org/10.1155/2018/7210680.

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We study a nonlinear Choquard equation with weighted terms and critical Sobolev-Hardy exponent. We apply variational methods and Lusternik-Schnirelmann category to prove the multiple positive solutions for this problem.

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30

KAWAMURA, Kazuhiro. "Lusternik-Schnirelmann type invariants for Menger manifolds." Journal of the Mathematical Society of Japan 53, no. 3 (2001): 669–85. http://dx.doi.org/10.2969/jmsj/1213023729.

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31

Roitberg, Joseph. "The product formula for Lusternik–Schnirelmann category." Algebraic & Geometric Topology 1, no. 1 (2001): 491–502. http://dx.doi.org/10.2140/agt.2001.1.491.

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32

Scoville, Nicholas A. "Lusternik–Schnirelmann category and the connectivity ofX." Algebraic & Geometric Topology 12, no. 1 (2012): 435–48. http://dx.doi.org/10.2140/agt.2012.12.435.

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33

Ayala, R., Eladio Domínguez Murillo, Alberto Márquez Pérez, and A. Quintero. "Lusternik-Schnirelmann invariants in proper homotopy theory." Pacific Journal of Mathematics 153, no. 2 (1992): 201–15. http://dx.doi.org/10.2140/pjm.1992.153.201.

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34

Matumoto, Takao. "Lusternik-Schnirelmann Category of Ribbon Knot Complement." Proceedings of the American Mathematical Society 114, no. 3 (1992): 873. http://dx.doi.org/10.2307/2159418.

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35

Regidor-García, Antonio. "Proper Lusternik-Schnirelmann $\pi\sb 1$-categories." Hiroshima Mathematical Journal 36, no. 2 (2006): 175–202. http://dx.doi.org/10.32917/hmj/1166642299.

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36

Colman, Hellen, and Enrique Macias-Virgós. "Transverse Lusternik–Schnirelmann category of foliated manifolds." Topology 40, no. 2 (2001): 419–30. http://dx.doi.org/10.1016/s0040-9383(99)00067-1.

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37

Fonda, Alessandro. "Generalizing the Lusternik-Schnirelmann critical point theorem." Bulletin of the London Mathematical Society 51, no. 1 (2018): 25–33. http://dx.doi.org/10.1112/blms.12205.

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38

Colman, Hellen. "Transverse Lusternik–Schnirelmann category of Riemannian foliations." Topology and its Applications 141, no. 1-3 (2004): 187–96. http://dx.doi.org/10.1016/j.topol.2003.12.006.

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39

Iwase, Norio, and Akira Kono. "Lusternik-Schnirelmann category of $\mathbf{Spin}{(9)}$." Transactions of the American Mathematical Society 359, no. 04 (2006): 1517–27. http://dx.doi.org/10.1090/s0002-9947-06-04120-1.

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40

Srinivasan, Tulsi. "The Lusternik–Schnirelmann category of metric spaces." Topology and its Applications 167 (April 2014): 87–95. http://dx.doi.org/10.1016/j.topol.2014.03.009.

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41

Khalil, Assakta, and Abd Ghafur Bin Ahmad. "COMPLETELY REGULAR MAPS AND LUSTERNIK-SCHNIRELMANN CATEGORY." JP Journal of Geometry and Topology 21, no. 1 (2018): 65–73. http://dx.doi.org/10.17654/gt021010065.

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42

Scheerer, H., and D. Tanré. "Variation zum Konzept der Lusternik-Schnirelmann-Kategorie." Mathematische Nachrichten 207, no. 1 (1999): 183–94. http://dx.doi.org/10.1002/mana.1999.3212070109.

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43

Stanley, Donald. "On the Lusternik-Schnirelmann Category of Maps." Canadian Journal of Mathematics 54, no. 3 (2002): 608–33. http://dx.doi.org/10.4153/cjm-2002-022-6.

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AbstractWe give conditions which determine if cat of a map go up when extending over a cofibre. We apply this to reprove a result of Roitberg giving an example of a CW complex Z such that cat(Z) = 2 but every skeleton of Z is of category 1. We also find conditions when cat(f × g) < cat(f) + cat(g). We apply our result to show that under suitable conditions for rational maps f, mcat(f) < cat(f) is equivalent to cat(f) = cat(f × idSn). Many examples with mcat(f) < cat(f) satisfying our conditions are constructed. We also answer a question of Iwase by constructing p-local spaces X such t

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44

Ginzburg, Viktor L., and Başak Z. Gürel. "Lusternik–Schnirelmann theory and closed Reeb orbits." Mathematische Zeitschrift 295, no. 1-2 (2019): 515–82. http://dx.doi.org/10.1007/s00209-019-02361-2.

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45

Farber, M. "Lusternik--Schnirelman theory for closed 1-forms." Commentarii Mathematici Helvetici 75, no. 1 (2000): 156–70. http://dx.doi.org/10.1007/s000140050117.

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46

Ledzewicz, Urszula, and Stanislaw Walczak. "On the Lusternik theorem for nonsmooth operators." Nonlinear Analysis: Theory, Methods & Applications 22, no. 2 (1994): 121–28. http://dx.doi.org/10.1016/0362-546x(94)90029-9.

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47

Montejano, Luis. "Lusternik-Schnirelmann category and Hilbert cube manifolds." Topology and its Applications 27, no. 1 (1987): 29–35. http://dx.doi.org/10.1016/0166-8641(87)90055-1.

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48

Scheerer, Hans, Donald Stanley, and Daniel Tanré. "Fibrewise construction applied to Lusternik-Schnirelmann category." Israel Journal of Mathematics 131, no. 1 (2002): 333–59. http://dx.doi.org/10.1007/bf02785865.

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49

Matumoto, Takao. "Lusternik-Schnirelmann category and knot complement II." Topology 34, no. 1 (1995): 177–84. http://dx.doi.org/10.1016/0040-9383(94)e0016-d.

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50

CÁRDENAS, MANUEL, FRANCISCO F. LASHERAS, and ANTONIO QUINTERO. "Detecting cohomology classes for the proper LS category. The case of semistable 3-manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 152, no. 2 (2011): 223–49. http://dx.doi.org/10.1017/s0305004111000417.

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AbstractWe give sufficient conditions for the existence of detecting elements for the Lusternik–Schnirelmann category in proper homotopy. As an application we determine the proper LS category of some semistable one-ended open 3-manifolds.

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