Colloquium

of the CRC 1442 Geometry: Deformations and Rigidity

Tuesday, 15 July 2025
at 4:00 pm
in lecture hall M2

Euler characteristics, algebraic K-Theory and the Farrell-Jones conjecture

Speakers: Dr. Maxime Ramzi and Prof. Dr. Thomas Nikolaus

While algebraic K-theory has many applications and uses in modern algebra and arithmetic, its origins actually lie in geometric topology through Whithead's work on simple homotopy theory as well as the notion of Euler characteristics. We will review this in modern language, to elucidate the nature of simple homotopy types and a new multiplicativity statement for Euler chareacteristics. This will also lead to parametrized versions of results of West and Chapman through the use of Efimov-K-Theory. The key is a K-theoretic model of assembly maps which is of independent nature and should have many more applications in the future. Specifically in the context of the CRC we use it to study the Farrell—Jones conjecture utilizing a transfer of methods from the C^*-algebraic world.