Geodesic
Cohomological Rigidity of the Connected Sum of Three Real Projective Spaces
Informatics and Automation, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Tome 317 (2022), pp. 198-209.

Voir la notice de l'article provenant de la source Math-Net.Ru

A real toric manifold $X^{\Bbb R} $ is said to be cohomologically rigid over ${\Bbb Z} _2$ if every real toric manifold whose ${\Bbb Z} _2$-cohomology ring is isomorphic to that of $X^{\Bbb R} $ is actually diffeomorphic to $X^{\Bbb R} $. Not all real toric manifolds are cohomologically rigid over ${\Bbb Z} _2$. In this paper, we prove that the connected sum of three real projective spaces is cohomologically rigid over ${\Bbb Z} _2$.
Keywords: real toric variety, real toric manifold, cohomological rigidity. 
@article{TRSPY_2022_317_a9,
     author = {Suyoung Choi and Mathieu Vall\'ee},
     title = {Cohomological {Rigidity} of the {Connected} {Sum} of {Three} {Real} {Projective} {Spaces}},
     journal = {Informatics and Automation},
     pages = {198--209},
     publisher = {mathdoc},
     volume = {317},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2022_317_a9/}
}
TY  - JOUR
AU  - Suyoung Choi
AU  - Mathieu Vallée
TI  - Cohomological Rigidity of the Connected Sum of Three Real Projective Spaces
JO  - Informatics and Automation
PY  - 2022
SP  - 198
EP  - 209
VL  - 317
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2022_317_a9/
LA  - ru
ID  - TRSPY_2022_317_a9
ER  - 
%0 Journal Article
%A Suyoung Choi
%A Mathieu Vallée
%T Cohomological Rigidity of the Connected Sum of Three Real Projective Spaces
%J Informatics and Automation
%D 2022
%P 198-209
%V 317
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2022_317_a9/
%G ru
%F TRSPY_2022_317_a9
Suyoung Choi; Mathieu Vallée. Cohomological Rigidity of the Connected Sum of Three Real Projective Spaces. Informatics and Automation, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Tome 317 (2022), pp. 198-209. http://geodesic.mathdoc.fr/item/TRSPY_2022_317_a9/

[1] Billera L.J., Lee C.W., “A proof of the sufficiency of McMullen's conditions for $f$-vectors of simplicial convex polytopes”, J. Comb. Theory. Ser. A, 31:3 (1981), 237–255 | MR | Zbl

[2] Bosio F., Meersseman L., “Real quadrics in $\mathbf C^n$, complex manifolds and convex polytopes”, Acta math., 197:1 (2006), 53–127 | MR | Zbl

[3] Buchstaber V.M., Panov T.E., Toric topology, Math. Surv. Monogr., 204, Amer. Math. Soc., Providence, RI, 2015 | MR | Zbl

[4] Choi S., Masuda M., Oum S., “Classification of real Bott manifolds and acyclic digraphs”, Trans. Amer. Math. Soc., 369:4 (2017), 2987–3011 | MR | Zbl

[5] S. Choi, M. Masuda, and D. Y. Suh, “Rigidity problems in toric topology: A survey”, Proc. Steklov Inst. Math., 275 (2011), 177–190 | MR | Zbl

[6] Choi S., Panov T., Suh D.Y., “Toric cohomological rigidity of simple convex polytopes”, J. London Math. Soc. Ser. 2, 82:2 (2010), 343–360 | MR | Zbl

[7] Choi S., Park H., “Wedge operations and torus symmetries”, Tohoku Math. J. Ser. 2, 68:1 (2016), 91–138 | MR | Zbl

[8] Choi S., Park H., “Wedge operations and torus symmetries. II”, Can. J. Math., 69:4 (2017), 767–789 | MR | Zbl

[9] Choi S., Park H., “Small covers over wedges of polygons”, J. Math. Soc. Japan, 71:3 (2019), 739–764 | MR | Zbl

[10] Choi S., Vallée M., An algorithmic strategy for finding characteristic maps over wedged simplicial complexes, E-print, 2021, arXiv: 2111.07298 [math.GT] | MR

[11] Davis M.W., Januszkiewicz T., “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62:2 (1991), 417–451 | MR | Zbl

[12] N. Yu. Erokhovets, “Moment–angle manifolds of simple $n$-polytopes with $n+3$ facets”, Russ. Math. Surv., 66:5 (2011), 1006–1008 | MR | Zbl

[13] Ishida H., Fukukawa Y., Masuda M., “Topological toric manifolds”, Moscow Math. J., 13:1 (2013), 57–98 | MR | Zbl

[14] Kamishima Y., Masuda M., “Cohomological rigidity of real Bott manifolds”, Algebr. Geom. Topol., 9:4 (2009), 2479–2502 | MR | Zbl

[15] Mani P., “Spheres with few vertices”, J. Comb. Theory. Ser. A, 13:3 (1972), 346–352 | MR | Zbl

[16] M. Masuda, “Cohomological non-rigidity of generalized real Bott manifolds of height 2”, Proc. Steklov Inst. Math., 268 (2010), 242–247 | MR | Zbl

[17] M. Masuda and T. E. Panov, “Semifree circle actions, Bott towers and quasitoric manifolds”, Sb. Math., 199:8 (2008), 1201–1223 | MR | Zbl

[18] Masuda M., Suh D.Y., “Classification problems of toric manifolds via topology”, Toric topology: Proc. Int. Conf., Osaka, 2006, Contemp. Math., 460, Amer. Math. Soc., Providence, RI, 2008, 273–286 | MR | Zbl