**Algebraic and geometric converses of the Seifert-van Kampen Theorem**

The classical Seifert-van Kampen theorem expresses the fundamental group
of a union of topological spaces as an amalgamated free product. An
amalgamated free product structure on the fundamental group of a
manifold can be realized by a codimension 1 submanifold, by geometric
transversality. The talk will describe an algebraic analogue of
transversality which decomposes modules and quadratic forms over an
amalgamated free product of rings.

*Andrew Ranicki*

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