Summary: Frobenius Algebra Structures
in Topological Quantum Field Theory
and Quantum Cohomology
by
Lowell Abrams
A dissertation submitted to The Johns Hopkins University
in conformity with the requirements for the degree of
Doctor of Philosophy
Baltimore, Maryland
1997

Abstract
We prove that a commutative finite­dimensional algebra A is a Frobenius
algebra if and only if it has a cocommutative comultiplication with counit.
Based on this, we prove the one­to­one correspondence between topological
quantum field theories and Frobenius algebras, formulated as an equivalence
of monoidal categories. For each Frobenius algebra A we define a canonical
``characteristic class,'' and show that this characteristic class is a unit if and
only if A is semisimple.
In quantum cohomology, the Frobenius algebra characteristic class, the

Source: Abrams, Lowell - Department of Mathematics, George Washington University

Collections: Mathematics