Coincidence theory for infra-nilmanifolds

Expanding Maps on Infra-nilmanifolds of Homogeneous Type

In this paper we investigate expanding maps on infra-nilmanifolds. Such manifolds are obtained as a quotient E\L, where L is a connected and simply connected nilpotent Lie group and E is a torsion-free uniform discrete subgroup of LoC, with C a compact subgroup of Aut(L). We show that if the Lie algebra of L is homogeneous (i.e., graded and generated by elements of degree 1), then the correspon...

Lefschetz and Nielsen Coincidence Numbers on Nilmanifolds and Solvmanifolds

Suppose M 1 ; M 2 are compact, connected orientable manifolds of the same dimension. Then for all pairs of maps f,g:M 1 ?! M 2 , the Nielsen coincidence number N(f,g) and the Lefschetz coincidence number L(f,g) are measures of the number of coincidences of f and g: points x 2 M 1 with f(x) = g(x). A manifold is a nilmanifold (solvmanifold) if it is a homogeneous space of a nilpotent (solvable) ...

Lefschetz and Nielsen Coincidence Numbers on Nilmanifolds and Solvmanifolds, Ii

In 10], it was claimed that Nielsen coincidence numbers and Lefschetz coincidence numbers are related by the inequality N (f; g) jL(f; g)j for all maps f; g : S 1 ! S 2 between compact orientable solvmanifolds of the same dimension. It was further claimed that N (f; g) = jL(f; g)j when S 2 is a nilmanifold. A mistake in that paper has been discovered. In this paper, that mistake is partially re...

Coincidence theory for compact morphisms

Generalized coincidence theory for set-valued maps

This paper presents a coincidence theory for general classes of maps based on the notion of a Φ-essential map (we will also discuss Φ-epi maps). c ©2017 All rights reserved.