Linking forms and maps of odd prime order
Authors:
J. P. Alexander, G. C. Hamrick and J. W. Vick
Journal:
Trans. Amer. Math. Soc. 221 (1976), 169185
MSC:
Primary 57E15; Secondary 57D85
MathSciNet review:
0402786
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Abstract: A differentiable orientation preserving map of odd prime period on a closed oriented differentiable manifold gives rise to two invariants taking values in a Witt group of bilinear forms. One is globally defined in terms of the rational cohomology of the manifold and the other is locally defined in terms of the fixed point set and its normal bundle. We show that these two invariants are, in fact, equal and apply this result to relate the structure of the manifold to that of the fixed point set and the quotient space.
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J. P. Alexander and G. C. Hamrick, The torsion Gsignature theorem for odd order groups (in preparation).
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W. Vick, The signature of the fixed set of a
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 J. P. Alexander, A invariant for orientation preserving involutions, Proc. Amer. Math. Soc. 51 (1975), 455460. MR 0377947 (51:14116)
 [2]
 J. P. Alexander and G. C. Hamrick, The torsion Gsignature theorem for odd order groups (in preparation).
 [3]
 J. P. Alexander, P. E. Conner, G. C. Hamrick and J. W. Vick, Witt classes of integral representations of an abelian pgroup, Bull. Amer. Math. Soc. 80 (1974), 11791182. MR 0384912 (52:5782)
 [4]
 J. P. Alexander, G. C. Hamrick and J. W. Vick, Bilinear forms and cyclic group actions, Bull. Amer. Math. Soc. 80 (1974), 730734. MR 0346821 (49:11545)
 [5]
 , The signature of the fixed set of a map of odd period, Proc. Amer. Math. Soc. (to appear). MR 0407862 (53:11632)
 [6]
 P. E. Conner, Some applications of the formula, Semigroup Forum (to appear).
 [7]
 P. E. Conner and E. E. Floyd, Maps of odd period, Ann. of Math. (2) 84 (1966), 132156. MR 34 #3587. MR 0203738 (34:3587)
 [8]
 P. E. Conner and F. Raymond, A quadratic form on the quotient of a periodic map, Semigroup Forum 7 (1974), 310333. MR 0391139 (52:11961)
 [9]
 J. Milnor and D. Husemoller, Symmetric bilinear forms, Ergebnisse der Mathematik, SpringerVerlag, Berlin and New York, 1973. MR 0506372 (58:22129)
 [10]
 C. T. C. Wall, Quadratic forms on finite groups and related topics, Topology 2 (1963), 281298. MR 28 #133. MR 0156890 (28:133)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719760402786X
PII:
S 00029947(1976)0402786X
Article copyright:
© Copyright 1976
American Mathematical Society
