12 citations · 41 across the 17 of their papers we have counts for
20 papers
The eigenvalue one property of finite groups, II
Gerhard Hiss, Rafał Lutowski
We prove a conjecture of Dekimpe, De Rock and Penninckx concerning the existence of eigenvalues one in certain elements of finite groups acting irreducibly on a real vector space o…
The eigenvalue one property of finite groups, I
Gerhard Hiss, Rafał Lutowski
We prove a conjecture of Dekimpe, De Rock and Penninckx concerning the existence of eigenvalues one in certain elements of finite groups acting irreducibly on a real vector space o…
The -property of flat manifolds: Toward the eigenvalue one property of finite groups
Gerhard Hiss, Rafał Lutowski
We introduce a conjecture of Dekimpe, De Rock and Penninckx and sketch some major steps in its proof. This text presents an extended account of the talk of the first author given a…
Spinc structures on real Bott manifolds
Anna Gąsior, Rafał Lutowski
We give a necessary and sufficient condition for existence of spinc structures on real Bott manifolds.
Automorphism groups of combinatorial Hantzsche-Wendt groups
Rafał Lutowski, Andrzej Szczepański, Richard Weidmann
Combinatorial Hantzsche-Wendt groups were introduced by W. Craig and P.A. Linnell. Every such a group , where is a natural number, encodes the holonomy action of any …
Complex Vasquez invariant
Anna Gąsior, Rafał Lutowski
In 1970 Vasquez proved that to every finite group we can assign a natural number with the property that every flat manifold with holonomy is a total space of a fiber…
Minimal non-solvable Bieberbach groups
Rafał Lutowski, Andrzej Szczepański
It has been shown by several authors that there exists a non-solvable Bieberbach group of dimension . In this note we show that this is in fact a minimal dimension for such kin…
Spin-structures on real Bott manifolds with Kähler structure
Anna Gąsior, Rafał Lutowski
Let be a real Bott manifold with Kähler structure. Using Ishida characterization \cite{I11} we give necessary and sufficient condition for the existence of the spin-structure o…
Spin structures on Hantzsche-Wendt manifolds
Rafał Lutowski, Jerzy Popko, Andrzej Szczepański
Using a combinatorial description of Stiefel-Whitney classes of closed flat manifolds with diagonal holonomy representation, we show that no Hantzsche-Wendt manifold of dimension g…
Flat manifolds with holonomy representation of quaternionic type
Gerhard Hiss, Rafał Lutowski, Andrzej Szczepański
We are interested in the question of the existence of flat manifolds for which all -irreducible components of the holonomy representation are either absolutely irreducib…
Symmetries of complex flat manifolds
Marek Hałenda, Rafał Lutowski
In this article we show how to calculate the group of automorphisms of flat Kähler manifolds. Moreover we are interested in the problem of classification of such manifolds up to bi…
Retractability of solutions to the Yang-Baxter equation and -nilpotency of skew braces
E. Acri, R. Lutowski, L. Vendramin
Using Bieberbach groups we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution…
Flat manifolds with homogeneous holonomy representation
Rafał Lutowski
We show that a rational holonomy representation of any flat manifold except torus must have at least two non-equivalent irreducible subrepresentations. As an application we show th…
A short note about diffuse Bieberbach groups
Anna Gąsior, Rafał Lutowski, Andrzej Szczepański
We consider low dimensional diffuse Bieberbach groups. In particular we classify diffuse Bieberbach groups up to dimension 6. We also answer a question from [S. Kionke, J. Raimbaul…
Classification of spin structures on 4-dimensional almost-flat manifolds
Rafał Lutowski, Nansen Petrosyan, Andrzej Szczepański
Almost-flat manifolds were defined by Gromov as a natural generalisation of flat manifolds and as such share many of their properties. Similarly to flat manifolds, it turns out tha…
Spin structures of flat manifolds of diagonal type
Rafał Lutowski, Nansen Petrosyan, Jerzy Popko +1
For each integer at least two, we construct non-spin closed oriented flat manifolds with holonomy group and with the property that all of their finite proper co…
Irreducible euclidean representations of Fibonacci groups
Rafał Lutowski
We show that every Hantzsche-Wendt group is an epimorphic image of a certain Fibonacci group.
Spin structures on flat manifolds
Rafał Lutowski, Bartosz Putrycz
We present an algorithmic approach to the problem of existence of spin structures on flat manifolds. We apply our method in the cases of flat manifolds of dimensions 5 and 6.
Holonomy groups of flat manifolds with property
Rafał Lutowski, Andrzej Szczepański
Let be a flat manifold. We say that has property if the Reidemeister number for every homeomorphism In this paper, we investi…
Seven dimensional flat manifolds with cyclic holonomy
Rafał Lutowski
We classify (up to affine equivalence) all 7-dimensional flat manifolds with a cyclic holonomy group.