• Corpus ID: 244729552

Topological categories related to Fredholm operators: II. The analytic index

@inproceedings{Ivanov2021TopologicalCR,
  title={Topological categories related to Fredholm operators: II. The analytic index},
  author={Nikolai V. Ivanov},
  year={2021}
}
Naively, the analytic index of a family of self-adjoint Fredholm operators ought to be (an equivalence class of) the family of the kernels of these operators. The present paper is devoted to a rigorous version of this idea based on ideas of Segal as developed by the author in arXiv:2111.14313 [math.KT]. The resulting new definition of the analytic index makes sense under much weaker continuity assumptions than the Atiyah-Singer one and can be easily adjusted to families of operators in fibers… 
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We show that every graph continuous family of unbounded operators in a Hilbert space becomes Riesz continuous after multiplication by an appropriate family of unitaries. This result leads to two
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Topological categories related to Fredholm operators: I. Classifying spaces
In 1970s Segal outlined proofs of two theorems relating spaces of Fredholm and self-adjoint Fredholm operators with Quillen's constructions used to define higher algebraic K-theory. In the present
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