Due to higher ecological awareness and more stringent environmental laws the necessity of lowering the energy consumption of manufacturing plants rises. Therefore the possibility to optimize a planned production hall becomes more and more important. The research project INFO, a project of the Vienna University of Technology in cooperation with industry partners and supported by the FFG, the Aus...

Given a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental additive functor holds for all additive functors, like K-theory, cyclic homology, topological Hochschild homology, etc. Finally, we reduce this fundamental isomorphism conjecture to K-theoretic ones.

We establish the topological s-cobordism surgery sequence for any closed oriented 4-manifold X homotopy equivalent to a connected sum X1# · · ·#Xn such that each topological 4-manifold Xi has fundamental group Γi of class SA. As a corollary, given Γi in a subclass ECS, if Γi is torsionfree and π2(Xi)⊗ Z2 = 0 (e.g. Xi aspherical), then X is topologically s-rigid. An application is an s-fibering ...

We study topological spaces with a distinguished set of paths, called directed paths. Since these directed paths are generally not reversible, the directed homotopy classes of directed paths do not assemble into a groupoid, and there is no direct analog of the fundamental group. However, they do assemble into a category, called the fundamental category. We define models of the fundamental categ...

The topological fundamental group π1(P \C0) is isomorphic to the binary 3-dihedral group D̃3 := 〈 α, β | α = β = (αβ) 〉 of order 12 (cf. [11] [4; Chapter 4, §4]). In [1], Abhyankar studied the complement of the three cuspidal quartic over an algebraically closed field k of arbitrary characteristics. He showed that, if char k 6= 2, 3, then the tame fundamental group of the complement is isomorphi...

Fundamental group is one of the most important topological invariants for general manifolds, which can be directly used as manifolds classification. In this work, we provide a series of practical and efficient algorithms to compute fundamental groups for general 3-manifolds based on CW cell decomposition. The input is a tetrahedral mesh, while the output is symbolic representation of its first ...

All spaces are assumed to be locally path connected and semi-locally 1-connected. Let X be a connected topological group with identity e, and let p : X̃ → X be the universal cover of the underlying space of X. It follows easily from classical properties of lifting maps to covering spaces that for any point ẽ in X̃ with pẽ = e there is a unique structure of topological group on X̃ such that ẽ is th...