Toric polynomial generators in the unitary cobordism ring

Toric polynomial generators in the unitary cobordism ring

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Yury Ustinovsky , Princeton University
Fine Hall 214

It is well-known that the unitary cobordism ring Omega^* is isomorphic to the polynomial ring with one generator in every even degree. However explicit description of 'nice' representatives of the generators turns out to be a difficult problem. In this talk we aim at constructing connected algebraic toric polynomial generators of Omega^*. Recently large progress in this problem was obtained by Andrew Wilfong: he provided polynomial generators in all odd dimensions and dimensions one less than prime power.  We resolve the problem in the remaining dimensions by applying certain birational equivariant modifications to the P^k-bundles over P^{n-k} (generalized 2-stage Bott towers).