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Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups
 
Katsuhiko Kuribayashi Okayama University of Science, Okayama, Japan
Mamoru Mimura Okayama University, Okayama, Japan
Tetsu Nishimoto Kinki Welfare University, Fukusakicho Hyogo, Japan
Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups
eBook ISBN:  978-1-4704-0453-6
Product Code:  MEMO/180/849.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups
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Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups
Katsuhiko Kuribayashi Okayama University of Science, Okayama, Japan
Mamoru Mimura Okayama University, Okayama, Japan
Tetsu Nishimoto Kinki Welfare University, Fukusakicho Hyogo, Japan
eBook ISBN:  978-1-4704-0453-6
Product Code:  MEMO/180/849.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1802006; 85 pp
    MSC: Primary 55; 57;

    Let \(G\) be a compact, simply connected, simple Lie group. By applying the notion of a twisted tensor product in the senses of Brown as well as of Hess, we construct an economical injective resolution to compute, as an algebra, the cotorsion product which is the \(E_2\)-term of the cobar type Eilenberg-Moore spectral sequence converging to the cohomology of classifying space of the loop group \(LG\). As an application, the cohomology \(H^*(BLSpin(10); \mathbb{Z}/2)\) is explicitly determined as an \(H^*(BSpin(10); \mathbb{Z}/2)\)-module by using effectively the cobar type spectral sequence and the Hochschild spectral sequence, and further, by analyzing the TV-model for \(BSpin(10)\).

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. The mod 2 cohomology of $BLSO(n)$
    • 3. The mod 2 cohomology of $BLG$ for $G=Spin(n)\ (7\le n\le 9)$
    • 4. The mod 2 cohomology of $BLG$ for $G=G_2, F_4$
    • 5. A multiplication on a twisted tensor product
    • 6. The twisted tensor product associated with $H^*(Spin(N);\mathbb {Z}/2)$
    • 7. A manner for calculating the homology of a DGA
    • 8. The Hochschild spectral sequence
    • 9. Proof of Theorem 1.6
    • 10. Computation of a cotorsion product of $H^*(Spin(10);\mathbb {Z}/2)$ and the Hochschild homology of $H^*(BSpin(10);\mathbb {Z}/2)$
    • 11. Proof of Theorem 1.7
    • 12. Proofs of Proposition 1.9 and Theorem 1.10
    • 13. Appendix
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1802006; 85 pp
MSC: Primary 55; 57;

Let \(G\) be a compact, simply connected, simple Lie group. By applying the notion of a twisted tensor product in the senses of Brown as well as of Hess, we construct an economical injective resolution to compute, as an algebra, the cotorsion product which is the \(E_2\)-term of the cobar type Eilenberg-Moore spectral sequence converging to the cohomology of classifying space of the loop group \(LG\). As an application, the cohomology \(H^*(BLSpin(10); \mathbb{Z}/2)\) is explicitly determined as an \(H^*(BSpin(10); \mathbb{Z}/2)\)-module by using effectively the cobar type spectral sequence and the Hochschild spectral sequence, and further, by analyzing the TV-model for \(BSpin(10)\).

  • Chapters
  • 1. Introduction
  • 2. The mod 2 cohomology of $BLSO(n)$
  • 3. The mod 2 cohomology of $BLG$ for $G=Spin(n)\ (7\le n\le 9)$
  • 4. The mod 2 cohomology of $BLG$ for $G=G_2, F_4$
  • 5. A multiplication on a twisted tensor product
  • 6. The twisted tensor product associated with $H^*(Spin(N);\mathbb {Z}/2)$
  • 7. A manner for calculating the homology of a DGA
  • 8. The Hochschild spectral sequence
  • 9. Proof of Theorem 1.6
  • 10. Computation of a cotorsion product of $H^*(Spin(10);\mathbb {Z}/2)$ and the Hochschild homology of $H^*(BSpin(10);\mathbb {Z}/2)$
  • 11. Proof of Theorem 1.7
  • 12. Proofs of Proposition 1.9 and Theorem 1.10
  • 13. Appendix
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