In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X...

space Kakutani fixed-point theorem Kleene fixed-point theorem Knaster–Tarski theorem Lefschetz fixed-point theorem Nielsen fixed-point theorem Poincaré–Birkhoff...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

Atiyah–Bott fixed-point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed-point theorem for smooth...

in 1925 and the American Philosophical Society in 1929. The Lefschetz fixed-point theorem, now a basic result of topology, was developed by him in papers...

have a fixed point, but it doesn't describe how to find the fixed point. The Lefschetz fixed-point theorem (and the Nielsen fixed-point theorem) from algebraic...

Holomorphic Lefschetz formula is an analogue for complex manifolds of the Lefschetz fixed-point formula that relates a sum over the fixed points of a...

zero when f has no fixed points, the Lefschetz–Hopf theorem trivially implies the Lefschetz fixed-point theorem. A. Katok and B. Hasselblatt(1995), Introduction...

algebraic topology, using the Lefschetz fixed-point theorem. Since the Betti numbers of a 2-sphere are 1, 0, 1, 0, 0, ... the Lefschetz number (total trace on...

instance in Lefschetz's fixed-point theorem. The Lefschetz number is a useful tool to find out whether a continuous function admits fixed-points. This...

instance in Lefschetz's fixed-point theorem. The Lefschetz number is a useful tool to find out whether a continuous function admits fixed-points. This...

introduced by Solomon Lefschetz (1926), at the same time introducing relative homology, for application to the Lefschetz fixed-point theorem. There are now numerous...

Grothendieck trace formula, an analogue in algebraic geometry of the Lefschetz fixed-point theorem in algebraic topology, used to express the Hasse–Weil zeta function...

(algebraic topology) Lefschetz fixed-point theorem (fixed points, algebraic topology) Lefschetz–Hopf theorem (topology) Leray–Hirsch theorem (algebraic topology)...

function with the diagonal may be computed using homology via the Lefschetz fixed-point theorem; the self-intersection of the diagonal is the special case of...

generalizations of the Lefschetz fixed-point theorem, with terms coming from fixed-point submanifolds of the group G. See also: equivariant index theorem. Atiyah (1976)...

theorem Freudenthal suspension theorem Hurewicz theorem Künneth theorem Lefschetz fixed-point theorem Leray–Hirsch theorem Poincaré duality theorem Seifert–van...

known as the Nielsen fixed-point theorem: Any map f has at least N(f) fixed points. Because of its definition in terms of the fixed-point index, the Nielsen...

Applications Jordan curve theorem Brouwer fixed point theorem Invariance of domain Lefschetz fixed-point theorem Hairy ball theorem Degree of a continuous...

infinite-dimensional spaces, topological degree theory, Jordan separation theorem, Lefschetz fixed-point theorem) Morse theory and Lusternik–Schnirelmann category theory...

characteristic of the circle (real projective line) is 0, and thus the Lefschetz fixed-point theorem says only that it must fix at least 0 points, but possibly more...

and to prove general results such as Poincaré duality and the Lefschetz fixed-point theorem in this context. Grothendieck originally developed étale cohomology...

occurs in the derivation of a probability density function; Lefschetz fixed-point theorem, where a telescoping sum arises in algebraic topology; Homology...

his work in developing K-theory, a generalized Lefschetz fixed-point theorem and the Atiyah–Singer theorem, for which he also won the Abel Prize jointly...

fixed-point theorem', a combination of the Riemann–Roch theorem and Lefschetz fixed-point theorem (it is named after Woods Hole, Massachusetts, the site...

mappings with finitely many fixed points is the Lefschetz-Hopf theorem. Since every vector field induces a flow on manifolds and fixed points of small flows...

Grothendieck trace formula is an analogue in algebraic geometry of the Lefschetz fixed-point theorem in algebraic topology. One application of the Grothendieck trace...

specific case of the K-theory of a stack.) A version of the Lefschetz fixed-point theorem holds in the setting of equivariant (algebraic) K-theory. Let...

{\displaystyle \operatorname {fix} (\varphi )} is finite, then by the Lefschetz fixed-point theorem, | fix ⁡ ( φ ) | = 1 − 2 tr ⁡ ( h ( φ ) ) + 1 = 2 − 2 tr ⁡ (...

fit into well-known patterns relating to Betti numbers, the Lefschetz fixed-point theorem and so on. The analogy with topology suggested that a new homological...