5 citations · 29 across the 15 of their papers we have counts for
15 papers
On geometric representation of -homology classes
Friedrich Hegenbarth, Dušan D. Repovš
In this chapter we give a geometric representation of classes, where is the -periodic surgery spectrum, by establishing a relationship between…
Limits of manifolds in the Gromov-Hausdorff metric space
Friedrich Hegenbarth, Dušan D. Repovš
We apply the Gromov-Hausdorff metric for characterization of certain generalized manifolds. Previously, we have proved that with respect to the metric generalized -…
Generalized manifolds, normal invariants, and -homology
Friedrich Hegenbarth, Dušan D. Repovš
Let be an arbitrary oriented closed generalized -manifold, . In our recent paper (Proc. Edinb. Math. Soc. (2) 63 (2020), no. 2, 597-607) we have constructed a ma…
On Steenrod -homology, generalized manifolds, and surgery
Friedrich Hegenbarth, Dušan Repovš
The aim of this paper is to show the importance of the Steenrod construction of homology theories for the disassembly process in surgery on a generalized -manifold , in ord…
Controlled surgery and -homology
Friedrich Hegenbarth, Dušan Repovš
This paper presents an alternative approach to controlled surgery obstructions. The obstruction for a degree one normal map with control map $q: X^n \r…
The relationship of generalized manifolds to Poincaré duality complexes and topological manifolds
Friedrich Hegenbarth, Dušan Repovš
The primary purpose of this paper concerns the relation of (compact) generalized manifolds to finite Poincaré duality complexes (PD complexes). The problem is that an arbitrary gen…
Homotopy classification of -complexes relative an order relation
Mehmetcik Pamuk, Friedrich Hegenbarth, Dušan Repovš
We define an order relation among oriented -complexes. We show that with respect to this relation, two -complexes over the same complex are homotopy equivalent if and o…
s-Cobordism classification of -manifolds through the group of homotopy self-equivalences
Friedrich Hegenbarth, Mehmetcik Pamuk, Dušan Repovš
The aim of this paper is to give an -cobordism classification of topological -manifolds in terms of the standard invariants using the group of homotopy self-equivalences. Ham…
Controlled homotopy equivalences and structure sets of manifolds
Friedrich Hegenbarth, Dušan D. Repovš
For a closed topological --manifold and a map inducing an isomorphism , there is a canonicaly defined morphism $b:H_{n+1}(B,K,\mathbb{L})\to \mat…
On minimal Poincaré -complexes
Alberto Cavicchioli, Friedrich Hegenbarth, Dušan Repovš
We consider two types of minimal Poincaré -complexes. One is defined with respect to the degree -map order. This idea was already present in our previous papers, and more sys…
Browder-Livesay filtrations and the example of Cappell and Shaneson
Friedrich Hegenbarth, Yuri V. Muranov, Dušan Repovš
Let be a 3-dimensional manifold with fundamental group which contains a quaternion subgroup of order 8. In 1979 Cappell and Shaneson constructed a nontrivial nor…
Surgery in codimension 3 and the Browder--Livesay invariants
Friedrich Hegenbarth, Yurij V. Muranov, Dušan Repovš
The inertia subgroup of a surgery obstruction group is generated by elements which act trivially on the set of homotopy triangulations $\Cal S(X)$ for some closed…
Some recent approaches in 4-dimensional surgery theory
Friedrich Hegenbarth, Dušan Repovš
It is well-known that an n-dimensional Poincaré complex , , has the homotopy type of a compact topological -manifold if the total surgery obstruction vani…
Applications of controlled surgery in dimension 4: Examples
Friedrich Hegenbarth, Dušan Repovš
The validity of Freedman's disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true…
The Bryant-Ferry-Mio-Weinberger construction of generalized manifolds
Friedrich Hegenbarth, Dušan Repovš
Following Bryant, Ferry, Mio and Weinberger we construct generalized manifolds as limits of controlled sequences p_i: X_i --> X_{i-1} : i = 1,2,... of controlled Poincaré spaces. T…