We find some restrictions on the intersection forms of smooth definite manifolds bounded by rational homology spheres which are rationally cobordant to lens spaces. As a first consequence, we show that several natural maps to the rational homology cobordism group have infinite rank cokernels. Further, we show that there is no $n$ such that every lens space smoothly embeds in $n$ copies of the complex projective plane. This is joint work with Paolo Aceto and Daniele Celoria.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/9096