An Elementary Differential Extension of Odd K-theory

نویسندگان

  • THOMAS TRADLER
  • SCOTT O. WILSON
چکیده

There is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an abelian group under ordinary block sum of matrices. This construction is functorial, and defines a differential extension of odd K-theory, fitting into natural commutative diagrams and exact sequences involving K-theory and differential forms. To prove this we obtain along the way several results concerning even and odd Chern and ChernSimons forms.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Inverse Galois Problem for Nilpotent Groups of Odd Order

Consider any nilpotent group G of finite odd order. We ask if we can always find a galois extension K of Q such that Gal(K/Q) ∼= G. This is the famous Inverse Galois Problem applied to nilpotent groups of finite odd order. By solving the Group Extension Problem and the Embedding Problem, two problems that are related to the Inverse Galois Problem, we show that such a K always exists. A major re...

متن کامل

A Loop Group Extension of the Odd Chern Character

We show that the universal odd Chern form, defined on the stable unitary group U , extends to the loop group LU as an equivariantly closed differential form. This provides an odd analogue to the Bismut-Chern form that appears in supersymmetric field theories. We also describe the associated transgression form, the so-called Bismut-Chern-Simons form, and explicate some properties it inherits as ...

متن کامل

Interpretations and differential Galois extensions. DRAFT

We give model-theoretic accounts and proofs of the following results: Suppose ∂y = Ay is a linear differential equation over a differential field K of characteristic 0, and the field CK of constants of K is existentially closed in K. Then: (i) There exists a Picard-Vessiot extension L of K, namely a differential field extension L of K which is generated by a fundamental system of solutions of t...

متن کامل

The extension algebra of some cohomological Mackey functors

Let k be a field of characteristic p. We construct a new inflation functor for cohomological Mackey functors for finite groups over k. Using this inflation functor, we give an explicit presentation of the graded algebra of self extensions of the simple functor S 1 , when p is odd and G is an elementary abelian p-group. AMS Subject Classification : 18A25, 18G10, 18G15, 20J05.

متن کامل

Analyzing the Role of Motivation Factors in Herzberg’s Theory on Teacher’s Job Satisfaction (Case Study: Elementary Schools in Talesh City)

Objective: The purpose of this study was to analyzing the role of motivation factors in Herzberg’s theory on teacher’s job satisfaction. Methods: The population of this study consisted of elementary school teachers in Talesh city (N=850), that 265 of them selected as the sample by using the systematic random sampling. The data collection tool was questionnaire that it's  face and content validi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012