| Full text | |
| Author(s): |
Pergher, Pedro L. Q.
;
Ramos, Adriana
Total Authors: 2
|
| Document type: | Journal article |
| Source: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. N/A, p. 9-pg., 2022-04-08. |
| Abstract | |
Consider the real, complex and quaternionic n-dimensional projective spaces, RPn, CPn and HPn to unify notation, write KdPn for the real (d = 1), complex (d = 2) and quaternionic (d = 4) n-dimensional projective space. Consider a pair (M, T), where M is a closed smooth manifold and T is a smooth involution defined on M. Write F for the fixed point set of T. In this paper we obtain the equivariant cobordism classification of the pairs (M, T) when F is of the form F = KdPm boolean OR KePn, with d < e, in the cases (m, n) = (odd, odd) and (m, n) = (odd, even). As will be seen in the history described in Sect. 1, the case F = a disjoint union of projective spaces has an intense and still unfinished history in the literature; in particular, there are several results in the literature in which F is the union of two projective spaces, but with d = e; our paper is the first to consider unions of projective spaces under different rings. For example, if d = e, in the case (m, n) = (odd, odd) all involution bounds, while for different rings there are nonbounding involutions. (AU) | |
| FAPESP's process: | 16/24707-4 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |