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), 169-185

MSC:
Primary 57E15; Secondary 57D85

MathSciNet review:
0402786

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**John P. Alexander,*A 𝑊(𝑍₂) invariant for orientation preserving involutions*, Proc. Amer. Math. Soc.**51**(1975), 455–460. MR**0377947**, 10.1090/S0002-9939-1975-0377947-3**[2]**J. P. Alexander and G. C. Hamrick,*The torsion G-signature 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 𝑝-group*, Bull. Amer. Math. Soc.**80**(1974), 1179–1182. MR**0384912**, 10.1090/S0002-9904-1974-13665-7**[4]**J. P. Alexander, G. C. Hamrick, and J. W. Vick,*Bilinear forms and cyclic group actions*, Bull. Amer. Math. Soc.**80**(1974), 730–734. MR**0346821**, 10.1090/S0002-9904-1974-13576-7**[5]**J. P. Alexander, G. C. Hamrick, and J. W. Vick,*The signature of the fixed set of a map of odd period*, Proc. Amer. Math. Soc.**57**(1976), no. 2, 327–331. MR**0407862**, 10.1090/S0002-9939-1976-0407862-9**[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), 132–156. MR**0203738****[8]**P. E. Conner and Frank Raymond,*A quadratic form on the quotient of a periodic map*, Semigroup Forum**7**(1974), no. 1-4, 310–333. Collection of articles dedicated to Alfred Hoblitzelle Clifford on the occasion of his 65th birthday and to Alexander Doniphan Wallace on the occasion of his 68th birthday. MR**0391139****[9]**John Milnor and Dale Husemoller,*Symmetric bilinear forms*, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 73. MR**0506372****[10]**C. T. C. Wall,*Quadratic forms on finite groups, and related topics*, Topology**2**(1963), 281–298. MR**0156890**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
57E15,
57D85

Retrieve articles in all journals with MSC: 57E15, 57D85

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1976-0402786-X

Article copyright:
© Copyright 1976
American Mathematical Society