I present an alternative way of computing the index of a Dirac operator on a manifold with boundary and a special family of pseudodifferential boundary conditions. The local version of this index theorem contains a number of divergence terms in the interior, which are higher order heat kernel invariants. I will present a way of associating boundary terms to those divergence terms, which are rather local of nature.
@article{JEDP_1998____A11_0, author = {Salomonsen, Gorm}, title = {Geometric heat kernel coefficient for APS-type boundary conditions}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, year = {1998}, pages = {1-19}, mrnumber = {99h:58180}, zbl = {01808720}, language = {en}, url = {http://dml.mathdoc.fr/item/JEDP_1998____A11_0} }
Salomonsen, Gorm. Geometric heat kernel coefficient for APS-type boundary conditions. Journées équations aux dérivées partielles, (1998), pp. 1-19. http://gdmltest.u-ga.fr/item/JEDP_1998____A11_0/
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