Essential maps and manifolds
HTML articles powered by AMS MathViewer
- by Jean-François Mertens PDF
- Proc. Amer. Math. Soc. 115 (1992), 513-525 Request permission
Abstract:
Let $(M,\partial M)$ be a compact $n$-manifold with boundary, orientable over a field $K$ with characteristic $q$. For $f:(Y,\partial Y) \to (M,\partial M)$, with $Y$ compact, and $(X,\partial X)$ a compact pair, $g:X \to M$, let $(P,\partial P) = \{ (y,x) \in Y \times (X,\partial X)|f(y) = g(x)\}$ denote the fibered product, with $p$ as the projection to $(X,\partial X)$. In Čech-cohomology with coefficients $K$, we show that if ${[unk]^n}(f)$ is injective then so is ${[unk]^*}(p)$—and a number of strengthenings, which point to a concept of $q$-essential map from one compact space to another.References
- Jean-François Mertens, Localization of the degree on lower-dimensional sets, Internat. J. Game Theory 32 (2003), no. 3, 379–386 (2004). Special issue on stable equilibria. MR 2082999, DOI 10.1007/s001820400164
- Jean-François Mertens, Stable equilibria—a reformulation. I. Definition and basic properties, Math. Oper. Res. 14 (1989), no. 4, 575–625. MR 1031202, DOI 10.1287/moor.14.4.575
- Jean-François Mertens, Stable equilibria—a reformulation. II. Discussion of the definition, and further results, Math. Oper. Res. 16 (1991), no. 4, 694–753. With errata to: “Stable equilibria—a reformulation. I. Definition and basic properties” [Math. Oper. Res. 14 (1989), no. 4, 575–625; MR1031202 (91b:90224)]. MR 1135046, DOI 10.1287/moor.16.4.694
- Colin Patrick Rourke and Brian Joseph Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin-New York, 1982. Reprint. MR 665919
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
- Ronald J. Stern, On topological and piecewise linear vector fields, Topology 14 (1975), no. 3, 257–269. MR 394659, DOI 10.1016/0040-9383(75)90007-5
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 513-525
- MSC: Primary 57N65; Secondary 55M25
- DOI: https://doi.org/10.1090/S0002-9939-1992-1116269-X
- MathSciNet review: 1116269