- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:09
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
15
2013
2
Semi-monotone sets
Saugata
Basu
Purdue University, WEST LAFAYETTE, UNITED STATES
Andrei
Gabrielov
Purdue University, WEST LAFAYETTE, UNITED STATES
Nicolai
Vorobjov
University of Bath, BATH, UNITED KINGDOM
o-minimal geometry, regular cell
A coordinate cone in $\mathbb R^n$ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of $\mathbb R^n$, definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone set is a topological regular cell.
Algebraic geometry
Manifolds and cell complexes
General
635
657
10.4171/JEMS/369
http://www.ems-ph.org/doi/10.4171/JEMS/369