We give a survey of algorithms for computing topological invariants of semialgebraic sets with special emphasis on the more recent developments in designing algorithms for computing the betti numbers of semialgebraic sets. This work is protected under by elsevier science, and the following. Resolved problems from this section may be found in. Online submissions on the journal home page are preferred, but it is possible to submit directly to the editor. An introduction to geometric topology dipartimento di matematica. Problems on lowdimensional topology, 2015 rims, kyoto. But at that time bill thurston was already starting to greatly in. Open problems in topology request pdf researchgate. This is a cumulative status report on the 1100 problems listed in the volume open problems in topology northholland, 1990, edited by j. The authors are among the world leaders in their respective research areas. Open problems in algebraic topology and homotopy theory. Open problems in topology ii edited by elliott pearl 2007 elsevier amsterdam boston new york oxford paris san diego san francisco singapore sydney tokyo. Pdf open problems on graphs arising from geometric.
Problems about the uniform structures of topological groups 361 chapter 39. Open problems in topology ii university of newcastle. Box 211, ae amsterdam the netherlands c 2007 elsevier science b. Here we discuss a number of unsolved problems in geometry of curves and. The outstanding problem then, in 4manifold topology, is to find if there is. I have made a note of some problems in the area of nonabelian algebraic topology and homological algebra in 1990, and in chapter 16 of the book in the same area and advertised here, with free pdf, there is a note of 32 problems and questions in this area which had occurred to me. Imp importance low, medium, high, outstanding rec recommended for undergraduates. Some open problem in low dimensional topology are maintained at the low dimen. This is a list of open problems on lowdimensional topology with. Lowdimensional and symplectic topology, volume 82 american. On some special classes of continuous maps 369 chapter 40. Request pdf open problems in topology this is a cumulative status report on the 1100 problems listed in the volume open problems in.
Resolved problems from this section may be found in solved problems. A list of open problems in differential geometry 1 can you hear an. It develops concepts that are useful and interesting on their own, like the sylvester matrix and resultants of polynomials. Open problems on graphs arising from geometric topology.
General topology, geometric topology, infinitedimensional topology, geometric group theory, functional analysis. Some open problem in low dimensional topology are maintained at thelow dimensional topology 3 page. These problems may well seem narrow, andor outofline of current trends, but i thought the latter big book. Open problems in topology edited by jan van mill free university amsterdam, the netherlands george m. Algorithmic semialgebraic geometry and topology recent. In april, 1977 when my rst problem list 38,kirby,1978 was nished, a good topologist could reasonably hope to understand the main topics in all of low dimensional topology. We interpret here the term geometric topology in a quite restrictive sense. Good open problems play an indispensable role in the development of dif ferential geometry. Finally numerous problems in all aspects of geometry are continually discussed. There are also growing lists of geometric problems onwikipedias unsolved problems 1 page. Thirty open problems in the theory of homogeneous continua 347 part 4. It concludes with a discussion of how problems in robots and computer vision can be framed in algebraic terms.1167 1302 34 701 929 928 846 407 1543 388 455 779 313 137 1439 650 1211 915 190 209 723 338 1402 1232 1533 172 214 585 1341 304 559 73 59 976 1288 595 1344 1012 1244 1434 1406 899 636 1175