Reidemeister Number in Lefschetz Fixed point theory
نویسندگان
چکیده
Several interesting numbers such as the homotopy invariant Lefschets number L(f), Nielsen N(f), fixed point index i(X, f,U) and Reidemeister R(f) play important roles in study of theorems. The gives more geometric information about points than other numbers. However is hard to compute general. To number, Jiang related it R(f ) induced homomorphism f : 1(X) when X a lens space or an H-space (Jian type space). For spaces, either N(f) = 0 if then which implies that homotopic free map. This review article discuss how these are theory.
منابع مشابه
The Lefschetz Principle , Fixed Point Theory , and Index Theory
This is a rough historical account of some uses of the Lefschetz Principle in fixed point theory and index theory. The Lefschetz Principle states that the alternating sum of the traces on cohomology (a global and rigid invariant) is equal to the alternating sum of the traces on the underlying cochain complex (a local and far less rigid invariant). The original Lefschetz Theorem for compact poly...
متن کاملThe Lefschetz Fixed Point Theorem
The Lefschetz Fixed Point Theorem generalizes a collection of fixed point theorems for different topological spaces, including maps on the n-sphere and the n-disk. Although the theorem is easily written in terms of compact manifolds, in this paper we will work entirely with topological spaces that are simplicial complexes or retracts of simplicial complexes. After developing the fundamentals of...
متن کاملAxioms for a local Reidemeister trace in fixed point and coincidence theory on differentiable manifolds
We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.
متن کاملGeneralized Lefschetz fixed point theorems in extension type spaces
Several Lefschetz fixed point theorems for compact type self maps in new classes of spaces are presented in this paper.
متن کاملMicrolocal study of Lefschetz fixed point formulas for higher - dimensional fixed point sets
We introduce new Lagrangian cycles which encode local contributions of Lefschetz numbers of constructible sheaves into geometric objects. We study their functorial properties and apply them to Lefschetz fixed point formulas with higherdimensional fixed point sets.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: 3C TIC
سال: 2022
ISSN: ['2254-6529']
DOI: https://doi.org/10.17993/3ctic.2022.112.61-70