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Realization of Numbers As the Degrees of Maps between Manifolds

Realization of Numbers As the Degrees of Maps between Manifolds
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摘要 We determine the set of degrees between some classes of oriented closed （n - 1）-connected 2n-manifolds by using the arithmetic theory of quadratic forms. We determine the set of degrees between some classes of oriented closed （n - 1）-connected 2n-manifolds by using the arithmetic theory of quadratic forms.
作者 Young Min LEE Fei XU
机构地区 Department of Mathematics School of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第8期1413-1424,共12页 数学学报（英文版）
基金 Supported by Morningside Center of Mathematics, National Natural Science Foundation of China (Grant Nos. 10325105 and 10531060) KRF (2003-070-C00001)
关键词 Oriented closed manifold degree of a map integral quadratic form Oriented closed manifold, degree of a map, integral quadratic form
分类号 O186.12 [理学—基础数学]
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参考文献10

  • 1Siegberg, H.: Brouwer degree: history and numerical computation. Numerical solution of highly non- linear problems, Sympos. Fixed Point Algorithms and Complementarity Problems, Univ. Southampton, Southampton, 1979, North-Holland, Amsterdam-New York, 1980, 389-411.
  • 2Siegberg, H.: Some historical remarks concerning degree theory. Amer. Math. Monthly, 88(2), 125-139 (1981).
  • 3Wall, C. T. C.: Classification of (n- 1)-connedcted 2n-manifolds. Ann. of Math., 75, 163-198 (1962).
  • 4Duan, H., Wang S.: Non-zero degree maps between 2n-manifolds. Acta Mathematica Sinica, English Series, 20, 1-14 (2004).
  • 5Duan, H., Wang, S.: The degrees of maps between manifolds. Math. Z., 244, 67-89 (2003).
  • 6Ding, Y. H., Pan, J. Z.: Computing degree of maps between manifolds. Acta Mathematica Sinica, English Series, 21, 1277-1284 (2005).
  • 7Colliot-Thelene, J.-L., Xu, F.: Brauer-Manin obstruction for integral points of homogeneous spaces and representations by integral quadratic forms. Compositio Math., 145, 309-363 (2009).
  • 8O'Meara, O. T.: Introduction to Quadratic Forms, Springer-Verlag, New York, 1973.
  • 9O'Meara, O. T.: The integral representations of quadratic forms over local fields. Amer. J. Math., 80, 843 -878 (1958).
  • 10Serre, J.-P.: A Course in Arithmetic, Springer-Verlag, New York, 1973.
Acta Mathematica Sinica,English Series
2010年 第8期

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