TY  - JOUR
A1  - Wallenta, Daniel
T1  - A Lefschetz fixed point formula for elliptic quasicomplexes
JF  - Integral equations and operator theor
N2  - In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.
KW  - Elliptic complexes
KW  - Fredholm complexes
KW  - Lefschetz number
Y1  - 2014
U6  - https://doi.org/10.1007/s00020-014-2122-4
SN  - 0378-620X
SN  - 1420-8989
VL  - 78
IS  - 4
SP  - 577
EP  - 587
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Wallenta, D.
T1  - Elliptic quasicomplexes on compact closed manifolds
JF  - Integral equations and operator theor
N2  - We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the zero section. We prove that elliptic quasicomplexes are Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes and prove a generalisation of the Atiyah-Singer index theorem.
KW  - Elliptic complexes
KW  - Fredholm complexes
KW  - Index theory
Y1  - 2012
U6  - https://doi.org/10.1007/s00020-012-1983-7
SN  - 0378-620X
VL  - 73
IS  - 4
SP  - 517
EP  - 536
PB  - Springer
CY  - Basel
ER  -