2 postings: a response regarding simplicial groups, and a change of registration deadline for the Euro-MTM...........DMD ____________________________________________________________- Date: Thu, 11 May 2000 12:16:42 +0100 (BST) From: "T.Porter" Subject: Re: query abt simpl gp actions In response to > Date: Fri, 05 May 2000 10:58:05 -0400 > From: "Steven R. Costenoble" > Subject: Query about simplicial group actions > > Is there a reference for basic facts about simplicial group actions on > simplicial sets? I've found several references to principal (free) > actions, but none that discuss, for example, the fact that in general > fixed-sets should not be taken level-wise. I can write down what I need, > but I'd like to save space and give credit where it's due. > > --Steve Costenoble > Steven.R.Costenoble@Hofstra.edu > A simplicial group is a group object in simplicial sets, so there is a considerable categorical literature at your disposal. A simplicial group action is a simplically enriched functor to the category of simplicial sets and as that category has all limits and colimits, the general theory (e.g. in Max Kelly's book on enriched category theory) handles a lot of the structure (fixed sets are enriched limits, orbit objects are enriched colimits). When looking at homotopy properties, much of the work of Dan Kan and his collaborators is relevant as is my own work on simplicially coherent category theory ((with Jean-Marc Cordier) Homotopy Coherent Category Theory, Trans. Amer. Math. Soc. 349 (1997) 1-54, and Categorical Aspects of Equivariant Homotopy, Proc. ECCT, Applied Cat.Structures.4 (1996) 195-212). Some of the references in these papers are also relevant. Tim. ************************************************************ Timothy Porter |tel direct: +44 1248 382492 Mathematics Division, |World Wide Web School of Informatics, |home page: http://www.bangor.ac.uk/~mas013/ University of Wales, Bangor |Mathematics and Knots : exhibition Dean St. |http://www.bangor.ac.uk/ma/CPM/ Bangor | Gwynedd LL57 1UT | United Kingdom | _____________________________________________________________ Date: Thu, 11 May 2000 11:38:59 +0200 From: Euro-MTM Subject: EURO-MTM: New deadline for registration. FIRST EURO MEDITERRANEAN TOPOLOGY MEETING Universitat Autonoma de Barcelona Bellaterra, July 4 to 7, 2000 http://mat.uab.es/euro-mtm - Period for registration has been extended until May 31, 2000. - Registration and accommodation forms are posted at http://mat.uab.es/euro-mtm. - CONTACT: Carles Broto e-mail: euro-mtm@mat.uab.es