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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 188–201 (Mi tm3350)  
This article is cited in 32 scientific papers (total in 32 papers)

Rigidity problems in toric topology: A survey

Suyoung Choia, Mikiya Masudab, Dong Youp Suhc

a Department of Mathematics, Ajou University, Suwon, Republic of Korea
b Department of Mathematics, Osaka City University, Osaka, Japan
c Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea
Full-text PDF (241 kB) Citations (32)
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Abstract: Several rigidity problems in toric topology are addressed in the survey paper by the second and third authors, “Classification Problems of Toric Manifolds via Topology” (in Toric Topology, Am. Math. Soc., Providence, RI, 2008, pp. 273–286). In the present paper, we survey the results on those problems including recent developments.
Received in May 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 275, Pages 177–190
DOI: https://doi.org/10.1134/S0081543811080128
Bibliographic databases:
Document Type: Article
UDC: 515.14+515.16
Language: English
Citation: Suyoung Choi, Mikiya Masuda, Dong Youp Suh, “Rigidity problems in toric topology: A survey”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 188–201; Proc. Steklov Inst. Math., 275 (2011), 177–190
Citation in format AMSBIB
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\by Suyoung~Choi, Mikiya~Masuda, Dong~Youp~Suh
\paper Rigidity problems in toric topology: A~survey
\inbook Classical and modern mathematics in the wake of Boris Nikolaevich Delone
\bookinfo Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth
\serial Trudy Mat. Inst. Steklova
\yr 2011
\vol 275
\pages 188--201
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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Linking options:
  • https://www.mathnet.ru/eng/tm3350
  • https://www.mathnet.ru/eng/tm/v275/p188
    • This publication is cited in the following 32 articles:
    1. Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller, “GKM manifolds are not rigid”, Algebr. Geom. Topol., 22:7 (2023), 3511  crossref
    2. Higashitani A., Kurimoto K., Masuda M., “Cohomological Rigidity For Toric Fano Manifolds of Small Dimensions Or Large Picard Numbers”, Osaka J. Math., 59:1 (2022), 177–215  mathscinet  isi
    3. Baralic D., Milenkovic L., “Small Covers and Quasitoric Manifolds Over Neighborly Polytopes”, Mediterr. J. Math., 19:2 (2022), 87  crossref  mathscinet  isi
    4. Suyoung Choi, Mathieu Vallée, “Cohomological Rigidity of the Connected Sum of Three Real Projective Spaces”, Proc. Steklov Inst. Math., 317 (2022), 178–188  mathnet  crossref  crossref  mathscinet
    5. Milena Pabiniak, Springer Proceedings in Mathematics & Statistics, 386, Interactions with Lattice Polytopes, 2022, 263  crossref
    6. Chen J., Lu Zh., Wu J., “Orbit Configuration Spaces of Small Covers and Quasi-Toric Manifolds”, Sci. China-Math., 64:1 (2021), 167–196  crossref  mathscinet  isi
    7. Yu L., Masuda M., “On Descriptions of Products of Simplices”, Chin. Ann. Math. Ser. B, 42:5 (2021), 777–790  crossref  mathscinet  isi  scopus
    8. Boyer Ch.P., Tonnesen-Friedman Ch.W., “Sasakian Geometry on Sphere Bundles”, Differ. Geom. Appl., 77 (2021), 101765  crossref  mathscinet  isi
    9. Choi S., Park H., “Multiplicative Structure of the Cohomology Ring of Real Toric Spaces”, Homol. Homotopy Appl., 22:1 (2020), 97–115  crossref  mathscinet  isi  scopus
    10. Baralic D. Grbic J. Limonchenko I. Vucic A., “Toric Objects Associated With the Dodecahedron”, Filomat, 34:7 (2020), 2329–2356  crossref  mathscinet  isi
    11. Boyer Ch.P., Calderbank D.M.J., Tonnesen-Friedman Ch.W., “The Kahler Geometry of Bott Manifolds”, Adv. Math., 350 (2019), 1–62  crossref  mathscinet  isi
    12. La Luz J., Allen D., “Certain Generalized Higher Derived Functors Associated to Quasitoric Manifolds”, J. Homotopy Relat. Struct., 13:2 (2018), 395–421  crossref  mathscinet  zmath  isi
    13. V. M. Buchstaber, N. Yu. Erokhovets, M. Masuda, T. E. Panov, S. Park, “Cohomological rigidity of manifolds defined by 3-dimensional polytopes”, Russian Math. Surveys, 72:2 (2017), 199–256  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. Choi S., Park S., “Strong Cohomological Rigidity of Toric Varieties”, Proc. R. Soc. Edinb. Sect. A-Math., 147:5 (2017), 971–992  crossref  mathscinet  zmath  isi
    15. Wiemeler M., “Equivariantly Homeomorphic Quasitoric Manifolds Are Diffeomorphic Dedicated to the Memory of Samuel Gitler”, Bol. Soc. Mat. Mex., 23:1, SI (2017), 501–509  crossref  mathscinet  zmath  isi
    16. Hasui Sh., Kishimoto D., “P-Local Stable Cohomological Rigidity of Quasitoric Manifolds”, Osaka J. Math., 54:2 (2017), 343–350  mathscinet  zmath  isi
    17. J. Grbić, S. Theriault, “Homotopy theory in toric topology”, Russian Math. Surveys, 71:2 (2016), 185–251  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. Choi S., Park S., “Projective bundles over toric surfaces”, Int. J. Math., 27:4 (2016), 1650032  crossref  mathscinet  zmath  isi  elib  scopus
    19. Bai Q., Li F., “Classification of Bott towers by matrix”, Front. Math. China, 11:2 (2016), 255–268  crossref  mathscinet  zmath  isi  scopus
    20. Dessai A., “Nonnegative Curvature, Low Cohomogeneity and Complex Cohomology”, Muenster J. Math., 9:1 (2016), 187–206  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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