X-Nico

unusual facts about Atiyah-Singer index theorem


Atiyah–Singer index theorem

In 1978 Constantine Callias, at the suggestion of his Ph.D. advisor Roman Jackiw, used the axial anomaly to derive this index theorem on spaces equipped with a Hermitian matrix called the Higgs field.


Affiliated operator

Later Atiyah and Singer showed that index theorems for elliptic operators on closed manifolds with infinite fundamental group could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group.

Dusa McDuff

Her career as a mathematician started picking up after her stint at MIT and soon she was accepted to the Institute for Advanced Study where she worked with Segal on the Atiyah–Segal completion theorem.

Ignatius III Atiyah

The synod proclaimed Ignatius III Atiyah as the only Patriarch, and Cyril Dabbas he was brought in chains to Ras-Baalbek and exiled near Hermel, where shortly later he was executed by men of the Emir.

KK-theory

It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem, and the classification of extensions of C*-algebras by Brown–Douglas–Fillmore (Lawrence G. Brown, Ronald G. Douglas, Peter Arthur Fillmore 1977).

Wave equation

The phenomenon of lacunas has been extensively investigated in Atiyah, Bott and Gårding (1970, 1973).


see also