Djordje Baralić, A Short Course on Quasitoric Manifolds

 
Djordje Baralić, Mathematical Institute SASA 
A Short Course on Quasitoric Manifolds 
Quasitoric manifolds were introduced in 1991 by M. Davis and T. 
Januszkiewicz as a topological analogue of the nonsingular projective 
toric variety of algebraic geometry. A smooth $2 n$-dimensional manifold 
is a quasitoric manifold if it admits a smooth, locally standard action of 
an $n$-dimensional torus, with orbit space an $n$-dimensional simple 
convex polytope. Since then they are extensively studied in the last 
decades because of their remarkable properties and applications in 
combinatorics, cobordisms, topology, etc. We present the basic facts and 
results about quasitoric manifolds and their real counterparts, the so 
caled ' small covers'.