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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Cubes of chain complexes, multi-complexes and totalisation

Presented by Thomas Huettemann , Queen's University Belfast

27 October 2014 16:00 in CM221

While the notion of a commutative cubical diagram of
chain complexes is quite obvious, it is far less clear what a homotopy
commutative cubical diagram should be. One possible definition is
obtained by demanding that its "totalisation", a graded module
equipped with a degree-shifting endomorphism, actually is a chain
complex. The resulting theory is used to define higher-dimensional
mapping tori, which will be employed to obtain a homological
characterisation of finite domination of chain complexes.

In some more detail, a chain complex is finitely dominated if it is
homotopy equivalent to a bounded complex of finitely generated
projective modules. Finite domination of a chain complex can be
characterised by vanishing of its "Novikov homology", that is, homology
with coefficients in certain formal Laurent series rings.

In the talk I will present joint work with David Quinn, relating the
homological machinery of homotopy commutative cubes with Novikov
homology and finite domination.

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