Cohomological Rigidity of the Connected Sum of Three Real Projective Spaces

Suyoung Choi ; Mathieu Vallée

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Tome 317 (2022), pp. 198-209

Résumé

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 ${\Bbb Z} _2$.

Détail

Keywords: real toric variety, real toric manifold, cohomological rigidity.