Slicing and intersection theory for chains modulo 𝜈 associated with real analytic varieties

Hardt, Robert M.

doi:10.1090/S0002-9947-1973-0338430-7

Slicing and intersection theory for chains modulo $\nu$ associated with real analytic varieties
HTML articles powered by AMS MathViewer

by Robert M. Hardt PDF

Trans. Amer. Math. Soc. 183 (1973), 327-340 Request permission

Abstract:

In a real analytic manifold a k dimensional (real) analytic chain is a locally finite sum of integral multiples of chains given by integration over certain k dimensional analytic submanifolds (or strata) of some k dimensional real analytic variety. In this paper, for any integer $\nu \geq 2$, the concepts and results of [6] on the continuity of slicing and the intersection theory for analytic chains are fully generalized to the modulo $\nu$ congruence classes of such chains.

References

F. J. Almgren Jr., Some interior regularity theorems for minimal surfaces and an extension of Bernstein’s theorem, Ann. of Math. (2) 84 (1966), 277–292. MR 200816, DOI 10.2307/1970520
F. J. Almgren Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure, Ann. of Math. (2) 87 (1968), 321–391. MR 225243, DOI 10.2307/1970587
Herbert Federer, Some theorems on integral currents, Trans. Amer. Math. Soc. 117 (1965), 43–67. MR 168727, DOI 10.1090/S0002-9947-1965-0168727-0
Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
Wendell H. Fleming, Flat chains over a finite coefficient group, Trans. Amer. Math. Soc. 121 (1966), 160–186. MR 185084, DOI 10.1090/S0002-9947-1966-0185084-5
Robert M. Hardt, Slicing and intersection theory for chains associated with real analytic varieties, Acta Math. 129 (1972), 75–136. MR 315561, DOI 10.1007/BF02392214

Homology of real analytic and semianalytic sets

Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, Vol. 27, American Mathematical Society, New York, 1942. MR 0007093, DOI 10.1090/coll/027
William P. Ziemer, Integral currents $\textrm {mod}$ $2$, Trans. Amer. Math. Soc. 105 (1962), 496–524. MR 150267, DOI 10.1090/S0002-9947-1962-0150267-3