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Search: MSC category 19K56 ( Index theory [See also 58J20, 58J22] )

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1. CMB Online first

De Nitties, Giuseppe; Schulz-Baldes, Hermann
Spectral Flows of Dilations of Fredholm Operators
Given an essentially unitary contraction and an arbitrary unitary dilation of it, there is a naturally associated spectral flow which is shown to be equal to the index of the operator. This result is interpreted in terms of the $K$-theory of an associated mapping cone. It is then extended to connect $\mathbb{Z}_2$ indices of odd symmetric Fredholm operators to a $\mathbb{Z}_2$-valued spectral flow.

Keywords:spectral flow, Fredholm operators, Z2 indices
Categories:19K56, 46L80

2. CMB 2000 (vol 43 pp. 37)

Bousaidi, M. A.
Multiplicative Structure of the Ring $K \bigl( S(T^*\R P^{2n+1}) \bigr)$
We calculate the additive and multiplicative structure of the ring $K\bigl(S(T^*\R P^{2n+1})\bigr)$ using the eta invariant.

Categories:19L64, 19K56, 55C35

3. CMB 2000 (vol 43 pp. 69)

Kaminker, Jerome; Perera, Vicumpriya
Type II Spectral Flow and the Eta Invariant
The relative eta invariant of Atiyah-Patodi-Singer will be shown to be expressible in terms of the notion of Type~I and Type~II spectral flow.

Categories:19K56, 46L80

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