TY - JOUR
T1 - Rational homotopy of mapping spaces between complex Grassmannians
AU - Gatsinzi, Jean Baptiste
AU - Otieno, Paul Antony
AU - Onyango-Otieno, Vitalis
N1 - Publisher Copyright:
© 2019 NISC (Pty) Ltd.
PY - 2019/4
Y1 - 2019/4
N2 - The complex Grassmann Gr(k, n) is the space of k dimensional subspaces of ℂ n . It is a complex manifold of complex dimension k(n − k). There is a natural inclusion i k ,n : Gr(k, n) ↪ Gr(k, n + r). In this paper, we use Sullivan models to compute the rational homotopy type of the component of the inclusion Gr(2, n) ↪ Gr(2, n + r) in the space of mappings from Gr(2, n) to Gr(2, n + r), r ≥ 1. We show in particular that map(Gr(2, n), Gr(2, n + 1); i n ) has the rational homotopy type of a product of odd spheres.
AB - The complex Grassmann Gr(k, n) is the space of k dimensional subspaces of ℂ n . It is a complex manifold of complex dimension k(n − k). There is a natural inclusion i k ,n : Gr(k, n) ↪ Gr(k, n + r). In this paper, we use Sullivan models to compute the rational homotopy type of the component of the inclusion Gr(2, n) ↪ Gr(2, n + r) in the space of mappings from Gr(2, n) to Gr(2, n + r), r ≥ 1. We show in particular that map(Gr(2, n), Gr(2, n + 1); i n ) has the rational homotopy type of a product of odd spheres.
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U2 - 10.2989/16073606.2019.1601139
DO - 10.2989/16073606.2019.1601139
M3 - Article
AN - SCOPUS:85064698228
SN - 1607-3606
VL - 43
SP - 1
EP - 12
JO - Quaestiones Mathematicae
JF - Quaestiones Mathematicae
IS - 8
ER -