Spectral Multiplicity and Odd K-theory

An Elementary Differential Extension of Odd K-theory

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...

K - theory of mapping class groups III : Odd torsion Luke

k-odd mean labeling of prism

‎a $(p‎,‎q)$ graph $g$ is said to have a $k$-odd mean‎ ‎labeling $(k ge 1)$ if there exists an injection $f‎ : ‎v‎ ‎to {0‎, ‎1‎, ‎2‎, ‎ldots‎, ‎2k‎ + ‎2q‎ - ‎3}$ such that the‎ ‎induced map $f^*$ defined on $e$ by $f^*(uv) =‎ ‎leftlceil frac{f(u)+f(v)}{2}rightrceil$ is a‎ ‎bijection from $e$ to ${2k - ‎‎‎1‎, ‎2k‎ + ‎1‎, ‎2k‎ + ‎3‎, ‎ldots‎, ‎2‎ ‎k‎ + ‎2q‎ - ‎3}$‎. ‎a graph that admits $k$...

SPECTRAL MULTIPLICITY FOR Gln(R)

We study the behavior of the cuspidal spectrum of T\^, where %? is associated to Gln(i?) and V is cofinite but not compact. By a technique that modifies the Lax-Phillips technique and uses ideas from wave equation techniques, if r is the dimension of JP, Na{k) is the counting function for the Laplacian attached to a Hilbert space Ha, Ma(X) is the multiplicity function, and Ho is the space of cu...

Relatively Spectral Morphisms and Applications to K-theory

Spectral morphisms between Banach algebras are useful for comparing their K-theory and their “noncommutative dimensions” as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral information is only known over a dense subalgebra. We investigate such relatively spectral morphisms. We prove a relative version of the Density Theorem regarding ...