Displaying similar documents to “On the fixed point formula for Atiyah and Bott”

Once More on the Lefschetz Fixed Point Theorem

Lech Górniewicz, Mirosław Ślosarski (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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An abstract version of the Lefschetz fixed point theorem is presented. Then several generalizations of the classical Lefschetz fixed point theorem are obtained.

Fixed point index theory for a class of nonacyclic multivalued maps

Zdzisław Dzedzej

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CONTENTS0. Introduction.....................................................................5I. Homology.........................................................................6II. Multivalued maps...........................................................11III. Chain approximations and index...................................15IV. Chain approximations of decompositions of maps........18V. Index of decompositions for compact polyhedra............26VI. Index of decompositions for compact...

Fixed point theory for homogeneous spaces, II

Peter Wong (2005)

Fundamenta Mathematicae

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Let G be a compact connected Lie group, K a closed subgroup and M = G/K the homogeneous space of right cosets. Suppose that M is orientable. We show that for any selfmap f: M → M, L(f) = 0 ⇒ N(f) = 0 and L(f) ≠ 0 ⇒ N(f) = R(f) where L(f), N(f), and R(f) denote the Lefschetz, Nielsen, and Reidemeister numbers of f, respectively. In particular, this implies that the Lefschetz number is a complete invariant, i.e., L(f) = 0 iff f is deformable to be fixed point free. This was previously...

Homological methods in fixed-point theory of multi-valued maps

Lech Górniewicz

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CONTENTS  Introduction................................................................. 5I. HOMOLOGY  1. Preliminaries............................................................. 7  2. Maps in spaces of finite type............................................. 9  3. The Čech homology functor with compact carriers........................... 11  4. Vietoris maps............................................................. 13  5. Homology of open subsets of Euclidean spaces.................................

Realization of fixed point sets of relative maps

Moo Ha Woo, Xuezhi Zhao (2011)

Fundamenta Mathematicae

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Given a relative map f: (X,A) → (X,A) on a pair (X,A) of compact polyhedra and a closed subset Y of X, we shall give some criteria for Y to be the fixed point set of some map relatively homotopic to f.