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Tautological rings for high-dimensional manifolds
(Cambridge University PressCompositio Mathematica, 2017-04)
We study tautological rings for high-dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^*$($M$) of those characteristic classes of smooth fibre bundles with fibre $M$ which is generated by generalised ...
Homological stability for moduli spaces of high dimensional manifolds. II
We prove a homological stability theorem for moduli spaces of manifolds
of dimension 2$\textit{n}$, for attaching handles of index at least $\textit{n}$, after these manifolds have been stabilised by countably many copies ...
Homological stability for moduli spaces of high dimensional manifolds. I
We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension 2n > 4, with respect to forming connected sum with S$^{n}$ x S$^{n}$ . This is analogous to Harer's stability theorem ...