A product formula for generalizations of the Kervaire invariant
HTML articles powered by AMS MathViewer
- by Edgar H. Brown
- Trans. Amer. Math. Soc. 216 (1976), 295-311
- DOI: https://doi.org/10.1090/S0002-9947-1976-0385896-5
- PDF | Request permission
Abstract:
Formulas are developed for the Arf invariant of the product of two manifolds in terms of invariants of the factors. If the Wu orientations are carefully chosen the formula is $\sigma (M \times N) = \sigma (M)\sigma (N)$.References
- William Browder, The Kervaire invariant of framed manifolds and its generalization, Ann. of Math. (2) 90 (1969), 157–186. MR 251736, DOI 10.2307/1970686
- William Browder, The Kervaire invariant, products and Poincaré transversality, Topology 12 (1973), 145–158. MR 326744, DOI 10.1016/0040-9383(73)90003-7
- Edgar H. Brown Jr. and Franklin P. Peterson, The Kervaire invariant of $(8k+2)$-manifolds, Amer. J. Math. 88 (1966), 815–826. MR 206970, DOI 10.2307/2373080
- Edgar H. Brown Jr., Generalizations of the Kervaire invariant, Ann. of Math. (2) 95 (1972), 368–383. MR 293642, DOI 10.2307/1970804
- Edgar H. Brown Jr., A product formula for an Arf-Kervaire invariant, Bull. Amer. Math. Soc. 80 (1974), 873–874. MR 356090, DOI 10.1090/S0002-9904-1974-13549-4
- Michel A. Kervaire, A manifold which does not admit any differentiable structure, Comment. Math. Helv. 34 (1960), 257–270. MR 139172, DOI 10.1007/BF02565940
- Shigeyuki Morita, On the Pontrjagin square and the signature, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 18 (1971), 405–414. MR 301744
- George W. Whitehead, Generalized homology theories, Trans. Amer. Math. Soc. 102 (1962), 227–283. MR 137117, DOI 10.1090/S0002-9947-1962-0137117-6
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 216 (1976), 295-311
- MSC: Primary 57D65
- DOI: https://doi.org/10.1090/S0002-9947-1976-0385896-5
- MathSciNet review: 0385896