Your language?
Sep, 2017
Sun Mon Tue Wed Thu Fri Sat
1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30

Real-oriented Cohomology Theories

ベクトル , による 2 2 つとき , その compatibility えるのは である その アイデア , Atiyah [ Ati66 ] によ Real K -theory として された

  • Atiyah Real K -theoy ( KR -theory)

KR -theory については , Karoubi [ Kar01 Kar02 ] などで している

Lie homogeneous space KR -theory , Seymour [ Sey73 ] 70 代前 ている では , Fok [ Fok14 ] compact Lie G G -equivariant KR -theory 調 べている

  • equivariant KR -theory

より Real-oriented cohomology theory については , Landweber [ Lan68 ] Araki Murayama [ AM78 ] えている

  • Real-oriented spectrum

としては , Real-oriented complex cobordism やそこから する spectrum があ Hu Kriz [ HK01 ] , Kitchloo Wilson [ KW07 KW08a KW08b ] , Banerjee [ Ban10 ] など

  • Real-complex cobordism MU
  • Real-Brown-Peterson spectrum BP
  • Real truncated Brown-Peterson spectrum BP n
  • Real-Jonshon-Wilson spectrum E ( n )

これらを いた Adams-Novikov spectral sequence もある Hu Kriz [ HK01 ] にある

Banerjee [ Ban14 ] E (2) 2 -action する homotopy fixed point spectrum ER (2) ている

Kitchloo Wilson [ KW15 ] ER ( n ) * ( BO ( q )) している

Kitchloo Lorman Wilson [ KLWa ] では , E ( n )-cohomology から ER ( n )-cohomology られるのはどのような , えられてい , [ KLWb ] では , E ( n ) 調 べている

Dotto thesis [ Dot ] によると , Real K -theory algebraic K -theory Hesselholt Madsen により えられているようである その 原稿 この から download できるようにな Høgenhaven [ Høg ] によると , topological Hochschild homology Real 導入 されているらしい Høgenhaven , topological cyclic homology Real えている

  • Real algebraic K -theory
  • Real topological Hochschild homology
  • Real topological cyclic homology

Greenlees Meier [ GM ] BP n E ( n ) Anderson dual 調 べて いる

References

[AM78]     Shôrô Araki and Mitutaka Murayama. τ -cohomology theories. Japan. J. Math. (N.S.) , 4(2):363–416, 1978.

[Ati66]     M. F. Atiyah. K -theory and reality. Quart. J. Math. Oxford Ser. (2) , 17:367–386, 1966, http://dx.doi.org/10.1093/qmath/17.1.367 .

[Ban10]     Romie Banerjee. Real Johnson-Wilson theories and non-immersions of projective spaces . ProQuest LLC, Ann Arbor, MI, 2010, arXiv:1204.4091 . Thesis (Ph.D.)–The Johns Hopkins University.

[Ban14]     Romie Banerjee. A modular description of ER (2). New York J. Math. , 20:743–758, 2014, arXiv:1212.2069 .

[Dot]     Emanuele Dotto. Stable real K -theory and real topological Hochschild homology, arXiv:1212.4310 .

[Fok14]     Chi-Kwong Fok. The real K -theory of compact Lie groups. SIGMA Symmetry Integrability Geom. Methods Appl. , 10:Paper 022, 26, 2014, arXiv:1308.3871 .

[GM]     J. P. C. Greenlees and Lennart Meier. Gorenstein duality for Real spectra, arXiv:1607.02332 .

[HK01]     Po Hu and Igor Kriz. Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence. Topology , 40(2):317–399, 2001, http://dx.doi.org/10.1016/S0040-9383(99)00065-8 .

[Høg]     Amalie Høgenhaven. Real topological cyclic homology of spherical group rings, arXiv:1611.01204 .

[Kar01]     Max Karoubi. A descent theorem in topological K -theory. K -Theory , 24(2):109–114, 2001, arXiv:math/0509396 .

[Kar02]     Max Karoubi. Equivariant K -theory of real vector spaces and real projective spaces. Topology Appl. , 122(3):531–546, 2002, arXiv:math/0509497 .

[KLWa]     Nitu Kitchloo, Vitaly Lorman, and W. Stephen Wilson. Landweber flat real pairs and ER ( n )-cohomology, arXiv:1603.06865 .

[KLWb]     Nitu Kitchloo, Vitaly Lorman, and W. Stephen Wilson. Multiplicative structure on Real Johnson-Wilson theory, arXiv:1701.00255 .

[KW07]     Nitu Kitchloo and W. Stephen Wilson. On the Hopf ring for ER ( n ). Topology Appl. , 154(8):1608–1640, 2007, http://dx.doi.org/10.1016/j.topol.2007.01.001 .

[KW08a]     Nitu Kitchloo and W. Stephen Wilson. The second real Johnson-Wilson theory and nonimmersions of RP n . Homology, Homotopy Appl. , 10(3):223–268, 2008, http://projecteuclid.org/euclid.hha/1251832474 .

[KW08b]     Nitu Kitchloo and W. Stephen Wilson. The second real Johnson-Wilson theory and nonimmersions of RP n . II. Homology Homotopy Appl. , 10(3):269–290, 2008, http://projecteuclid.org/euclid.hha/1251832475 .

[KW15]     Nitu Kitchloo and W. Stephen Wilson. The ER ( n )-cohomology of BO ( q ) and real Johnson-Wilson orientations for vector bundles. Bull. Lond. Math. Soc. , 47(5):835–847, 2015, arXiv:1409.1281 .

[Lan68]     Peter S. Landweber. Conjugations on complex manifolds and equivariant homotopy of MU . Bull. Amer. Math. Soc. , 74:271–274, 1968, http://dx.doi.org/10.1090/S0002-9904-1968-11917-2 .

[Sey73]     R. M. Seymour. The real K -theory of Lie groups and homogeneous spaces. Quart. J. Math. Oxford Ser. (2) , 24:7–30, 1973, http://dx.doi.org/10.1093/qmath/24.1.7 .