Pure Maths Colloquium: Bordisms and surgery theory (Joint work with Joerg Sixt)
10 October 2005 00:00 in CM221
"Roughly speaking, Wall's realisation theorem asserts that a certain class of bordisms is classified by an abelian group, $L_n(\pi)$, which depends only upon the dimension ($n > 4$) and fundamental group of the bordism. Wall's theorem plays an essential role in the classical surgery classification of manifolds within a given homotopy type. Kreck extended surgery theory, replacing $L$-groups with certain $l$-monoids to classify $n$-manifolds with a given $n/2$-type (weaker input that homotopy type). I shall explain our recent calculation of the odd dimensional $l$-monoids, our extensions of Wall's realisation theorem for even dimensional bordisms and some classification results which follow. "
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