Algebraic Topology of Manifolds

Date: 11 - 15 September 2017

Location: Mathematical Institute, University of Oxford

Manifolds are at the centre of much of geometry and topology, and through the influence of axiomatic topological quantum field theory they have become an important organizing force in category and representation theory.

Classically, in the 1960s, algebraic topology was at the heart of their classification theory in form of characteristic classes and characteristic numbers, cobordism theory, surgery theory, and later Waldhausen’s K-theory of manifolds. By the 1980s the machinery got heavy with diminishing returns. We are now experiencing a renaissance of the field as well as a paradigm shift where manifolds not only are the objects of study but become the tools.

The school aims at inspiring the next generation with this exciting success story of interwoven ideas bouncing between different fields, and giving the participants the tools to contribute to this lively research area.