The $K$-homology class of the Euler characteristic operator is trivial
نویسندگان
چکیده
منابع مشابه
The K-homology Class of the Euler Characteristic Operator Is Trivial
Abstract. On any manifold Mn, the de Rham operator D = d + d∗ (with respect to a complete Riemannian metric), with the grading of forms by parity of degree, gives rise by Kasparov theory to a class [D] ∈ KO0(M), which when M is closed maps to the Euler characteristic χ(M) in KO0(pt) = Z. The purpose of this note is to give a quick proof of the (perhaps unfortunate) fact that [D] is as trivial a...
متن کاملThe convexity of the integral operator on the class of the integral operator on the class B(mu,alpha)
In this paper, we study the convexity of the integral operator
متن کاملSecondary Characteristic Classes and the Euler Class
We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We then show that if X is a smooth affine scheme of dimension d over a field k of finite 2cohomological dimension (with char(k) 6= 2) and E is a rank d vector bundle over X , vanishing of the Chow-Witt theoretic Euler class of E is equivalent to vanishing of its top Chern class an...
متن کاملA Hochschild Homology Euler Characteristic for Circle Actions
Abstract. We define an “S -Euler characteristic”, χ̃S1 (X) , of a circle action on a compact manifold or finite complex X . It lies in the first Hochschild homology group HH1(ZG) where G is the fundamental group of X . This χ̃S1 (X) is analogous in many ways to the ordinary Euler characteristic. One application is an intuitively satisfying formula for the Euler class (integer coefficients) of the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04943-6