**Astérisque**

Volume: 333;
102 pp;
Softcover
**Print ISBN: 978-2-85629-293-8
Product Code: AST/333**

List Price: $45.00

AMS Member Price: $36.00

# Fixed Point Theory and Trace for Bicategories

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*Kate Ponto*

A publication of the Société Mathématique de France

The Lefschetz fixed point theorem follows easily from the
identification of the Lefschetz number with the fixed point index. This
identification is a consequence of the functoriality of the trace in symmetric
monoidal categories. There are refinements of the Lefschetz number and the
fixed point index that give a converse to the Lefschetz fixed point theorem. An
important part of this theorem is the identification of these different
invariants.

The author defines a generalization of the trace in symmetric
monoidal categories to a trace in bicategories with shadows. She shows
the invariants used in the converse of the Lefschetz fixed point theorem are
examples of this trace and that the functoriality of the trace provides some of
the necessary identifications. The methods used here do not use simplicial
techniques and so generalize readily to other contexts.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students and research mathematicians interested in fixed point theory.