Title:  Spin Cobordism and Wedge Quasitoric Manifolds

Abstract:  Quasitoric manifolds are smooth 2n-manifolds admitting a "nice" action of the compact n-torus so that the quotient of this action yields a (combinatorially) simple polytope.  They are a generalization of smooth projective toric variaties and much is known about these manifolds in terms of complex cobordism theory.  In fact they were used by Buchstaber and Panov to show that every cobordism complex class contains a (connected) quasitoric manifold.

Far less is known about spin quasitoric manifolds and spin cobordism which requires the calculation of KO-characteristic classes.  We consider a procedure developed to investigate topological data for spin quasitoric manfolds which utilizes a wedge polytope operation on the quotient polytope.  We'll discuss a list of results concerning these "wedge" quasitoric manifolds, including such topics as Bott manifolds, the connected sum, the Todd genus and lastly, specific criteria in terms of combinatorial data allowing for the calculation of KO-characteristic classes of spin quasitoric manifolds.