scholarly journals A note on the higher Atiyah–Patodi–Singer index theorem on Galois coverings

2016 ◽  
Vol 10 (1) ◽  
pp. 261-302 ◽  
Author(s):  
Alexander Gorokhovsky ◽  
Hitoshi Moriyoshi ◽  
Paolo Piazza
Keyword(s):  
Index Theorem ◽  
Galois Coverings

scholarly journals The relative L2 index theorem for Galois coverings

2021 ◽  
Vol 6 (3) ◽  
pp. 503-541
Author(s):  
Moulay-Tahar Benameur
Keyword(s):  
Index Theorem ◽  
Galois Coverings ◽  
L2 Index

Preliminaries

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Valued Fields ◽  
Definable Set ◽  
Valued Field ◽  
Galois Coverings ◽  
Definable Type ◽  
Definable Sets ◽  
Background Material

This chapter provides some background material on definable sets, definable types, orthogonality to a definable set, and stable domination, especially in the valued field context. It considers more specifically these concepts in the framework of the theory ACVF of algebraically closed valued fields and describes the definable types concentrating on a stable definable V as an ind-definable set. It also proves a key result that demonstrates definable types as integrals of stably dominated types along some definable type on the value group sort. Finally, it discusses the notion of pseudo-Galois coverings. Every nonempty definable set over an algebraically closed substructure of a model of ACVF extends to a definable type.

scholarly journals Index theorem on T2/ZN orbifolds

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Makoto Sakamoto ◽  
Maki Takeuchi ◽  
Yoshiyuki Tatsuta
Keyword(s):  
Index Theorem

scholarly journals An index theorem for super derivations

1989 ◽  
Vol 125 (1) ◽  
pp. 147-152
Author(s):  
Arthur Jaffe ◽  
Andrzej Lesniewski
Keyword(s):  
Index Theorem
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