scholarly journals On some applications of unstable Adams operations to the topology of Kac-Moody groups

2016 ◽  
Vol 145 (2) ◽  
pp. 915-924
Author(s):  
Nitu Kitchloo
Keyword(s):  
Adams Operations

Adams operations and integral Hermitian-Galois representations

1996 ◽  
Vol 118 (5) ◽  
pp. 925-962 ◽  
Author(s):  
David Burns ◽  
Ted Chinburg
Keyword(s):  
Galois Representations ◽  
Adams Operations

Adams operations on the virtual K-theory of ℙ(1,n)

2016 ◽  
Vol 16 (08) ◽  
pp. 1750149
Author(s):  
Takashi Kimura ◽  
Ross Sweet
Keyword(s):  
Cotangent Bundle ◽  
Crepant Resolution ◽  
Chern Classes ◽  
Localization Theorem ◽  
Virtual Line ◽  
Power Operations ◽  
Power Operation ◽  
K Theory ◽  
Line Elements ◽  
Adams Operations

We analyze the structure of the virtual (orbifold) [Formula: see text]-theory ring of the complex orbifold [Formula: see text] and its virtual Adams (or power) operations, by using the non-Abelian localization theorem of Edidin–Graham [D. Edidin and W. Graham, Nonabelian localization in equivariant [Formula: see text]-theory and Riemann–Roch for quotients, Adv. Math. 198(2) (2005) 547–582]. In particular, we identify the group of virtual line elements and obtain a natural presentation for the virtual [Formula: see text]-theory ring in terms of these virtual line elements. This yields a surjective homomorphism from the virtual [Formula: see text]-theory ring of [Formula: see text] to the ordinary [Formula: see text]-theory ring of a crepant resolution of the cotangent bundle of [Formula: see text] which respects the Adams operations. Furthermore, there is a natural subring of the virtual K-theory ring of [Formula: see text] which is isomorphic to the ordinary K-theory ring of the resolution. This generalizes the results of Edidin–Jarvis–Kimura [D. Edidin, T. J. Jarvis and T. Kimura, Chern classes and compatible power operation in inertial [Formula: see text]-theory, Ann. K-Theory (2016)], who proved the latter for [Formula: see text].

scholarly journals Groups of unstable Adams operations on p–local compact groups

2017 ◽  
Vol 17 (1) ◽  
pp. 355-418
Author(s):  
Ran Levi ◽  
Assaf Libman
Keyword(s):  
Compact Groups ◽  
Adams Operations
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