... OpenURL. Abstract: This article is intended to provide some new insights about concurrency th... more ... OpenURL. Abstract: This article is intended to provide some new insights about concurrency theory using ideas from geometry, and more specifically from algebraic topology. The aim of the paper is two-fold: we justify applications ...
ABSTRACT . The question whether every manifold admits a non-trivial group action has been answere... more ABSTRACT . The question whether every manifold admits a non-trivial group action has been answered to the negative already back in 1971. Several authors have given classes of examples of manifolds, on which no such symmetry" can exist. This survey describes a method showing the existence of symmetries on certain classes of simply-connected manifolds. It aims to explain a blend of methods from transformation group theory, deformation theory, rational homotopy and rational surgery. 1. Introduction: History and Motivation An old and intriguing question in transformation group theory is to whether one should expect a manifold to be symmetric. In more technical terms: Does a compact smooth manifold M always support a non-trivial (topological or smooth) action : GM !M of some compact Lie group G? Of course, it suces to consider (non)-existence of (eective) actions of cyclic groups on the manifold in question. In the period 1971-1981, several authors exhibited classes of non-symmetric manifolds ...
... CCR9821038. S. Rajsbaum (Ed.): LATIN 2002, LNCS 2286, pp. ... CED ∗ (X, Y ) = min{ed(X, σ k ... more ... CCR9821038. S. Rajsbaum (Ed.): LATIN 2002, LNCS 2286, pp. ... CED ∗ (X, Y ) = min{ed(X, σ k (Y )) | 0 ≤ k<m} (5) where ed denotes the edit distance, and σ k (Y ) is the cyclic shift of Y by k which is defined as follows: σ0(Y ) = Y , and for 0 <k<m, σ k (Y ) = yk+1 ...ymy1 ...yk. ...
... OpenURL. Abstract: This article is intended to provide some new insights about concurrency th... more ... OpenURL. Abstract: This article is intended to provide some new insights about concurrency theory using ideas from geometry, and more specifically from algebraic topology. The aim of the paper is two-fold: we justify applications ...
ABSTRACT . The question whether every manifold admits a non-trivial group action has been answere... more ABSTRACT . The question whether every manifold admits a non-trivial group action has been answered to the negative already back in 1971. Several authors have given classes of examples of manifolds, on which no such symmetry" can exist. This survey describes a method showing the existence of symmetries on certain classes of simply-connected manifolds. It aims to explain a blend of methods from transformation group theory, deformation theory, rational homotopy and rational surgery. 1. Introduction: History and Motivation An old and intriguing question in transformation group theory is to whether one should expect a manifold to be symmetric. In more technical terms: Does a compact smooth manifold M always support a non-trivial (topological or smooth) action : GM !M of some compact Lie group G? Of course, it suces to consider (non)-existence of (eective) actions of cyclic groups on the manifold in question. In the period 1971-1981, several authors exhibited classes of non-symmetric manifolds ...
... CCR9821038. S. Rajsbaum (Ed.): LATIN 2002, LNCS 2286, pp. ... CED ∗ (X, Y ) = min{ed(X, σ k ... more ... CCR9821038. S. Rajsbaum (Ed.): LATIN 2002, LNCS 2286, pp. ... CED ∗ (X, Y ) = min{ed(X, σ k (Y )) | 0 ≤ k<m} (5) where ed denotes the edit distance, and σ k (Y ) is the cyclic shift of Y by k which is defined as follows: σ0(Y ) = Y , and for 0 <k<m, σ k (Y ) = yk+1 ...ymy1 ...yk. ...
This monograph presents an application of concepts and methods from algebraic topology to models ... more This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis. Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs. The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than “just” the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account. The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.
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Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs.
The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than “just” the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account.
The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.