# 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…

## 3 Citations

Spectral sections: two proofs of a theorem of Melrose-Piazza

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- 2021

Spectral sections of families of self-adjoint Fredholm operators were introduced by Melrose and Piazza [MP1] for the needs of index theory. The basic result about spectral sections is a theorem of…

From graph to Riesz continuity

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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…

The continuity properties of discrete-spectrum families of Fredholm operators

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Introduction. Recently, N. Ivanov [I1] introduced notions of Fredholm families and discrete-spectrum families of self-adjoint Fredholm operators. Fredholm families are not (and probably cannot be)…

## References

SHOWING 1-10 OF 17 REFERENCES

Spectral sections: two proofs of a theorem of Melrose-Piazza

- Mathematics
- 2021

Spectral sections of families of self-adjoint Fredholm operators were introduced by Melrose and Piazza [MP1] for the needs of index theory. The basic result about spectral sections is a theorem of…

Leray theorems in bounded cohomology theory

- Mathematics
- 2020

The paper is devoted to a generalized and simplified version of author's approach to covering theorems in bounded cohomology theory. The amenability assumptions are replaced by weaker and more…

Twisted K-theory

- Mathematics
- 2004

Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C ∗ -algebras. Up to equivalence, the twisting…

Configuration-spaces and iterated loop-spaces

- Mathematics
- 1973

The object of this paper is to prove a theorem relating "configurationspaces" to iterated loop-spaces. The idea of the connection between them seems to be due to Boardman and Vogt [2]. Part of the…

Index theory for skew-adjoint fredholm operators

- Mathematics
- 1969

© Publications mathématiques de l’I.H.É.S., 1969, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…

Classifying spaces and spectral sequences

- Mathematics
- 1968

© Publications mathematiques de l’I.H.E.S., 1968, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.…

Champs continus d’espaces hilbertiens et de $C^\ast $ -algèbres

- Mathematics
- 1963

© Bulletin de la S. M. F., 1963, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord…

Topological categories related to Fredholm operators: I. Classifying spaces

- Mathematics
- 2021

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…