In this paper a set of Petri net equivalences is proposed. A correlation between all introduced equivalences is established, and a lattice of implications is obtained. In addition equivalences are examined on sequential nets. The process equivalences are demonstrated to be well discerning on this net class.

We develop a holomorphic equivalence between on one hand the space of pairs (stable bundle, flat connection bundle) and sheaf connections (the splittings one-jet sequence) for determinant (Quillen) line bundle over moduli vector bundles compact connected Riemann surface. This is shown to be holomorphically symplectic. The equivalences, both symplectic, seem quite general, in that they extend ot...

Behavioural equivalences on open systems are usually defined by comparing system behaviour in all environments. Due to this “universal” quantification over the possible hosting environments, such equivalences are often difficult to check in a direct way. Here, working in the setting of process calculi, we introduce a hierarchy of behavioural equivalences for open systems, building on a previous...

(P) where / is the complex /-homomorphism and , y denotes localization at p. Both J and ** are infinite loop maps, and it is natural to ask whether this result is infinitely deloopable; that is, whether J<ff = / as infinite loop maps. This is the Stable Adams Conjecture. We announce here two independent proofs of this conjecture. Details will appear in [2] and [6]. METHOD 1. Our proof is based ...

Introduction 150 Organization 152 Acknowledgments 152 1. Symmetric spectra 153 1.1. Simplicial sets 153 1.2. Symmetric spectra 154 1.3. Simplicial structure on Sp 156 1.4. Symmetric Ω-spectra 158 2. The smash product of symmetric spectra 159 2.1. Symmetric sequences 159 2.2. Symmetric spectra 162 2.3. The ordinary category of spectra 165 3. Stable homotopy theory of symmetric spectra 165 3.1. S...

This document consists of lecture notes for four lectures given by Brooke Shipley at the 2017 Young Topologists Meeting at the Swedish Royal Institute of Technology (KTH) in Stockholm, Sweden. The original conference abstract for the lecture series is below. This sequence of lectures will explore the connections between the differential graded world and the spectral world. There will first be a...

We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences. In particular, we show that the class of weak equivalences between simplicial sets is finitely accessible.