Abstract
Recent work of Mishchenko and Morales Meléndez (arXiv:1112.2104 [math.AT], 2011) has shed new light on the classical exact sequence of Conner and Floyd in G-equivariant bordism for a finite group G. This paper is primarily an exposition of the results obtained there as specialized to finite groups. For a countable discrete group G, there is a brief discussion of the generalization to the bordism theory of proper, cocompact G-manifolds.
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References
Atiyah M.F., Singer I.M.: The index of elliptic operators. III. Ann. of Math. 87, 546–604 (1968)
Bröcker Th., Jänich K.: Introduction to Differential Topology. Cambridge University Press, Cambridge (1982)
Conner P.E., Floyd E.E.: Differentiable Periodic Maps. Academic Press, New York (1964)
Conner P.E., Floyd E.E.: Periodic maps which preserve a complex structure. Bull. Amer. Math. Soc. 70, 574–579 (1964)
Costenoble S.R.: Unoriented bordism for odd-order groups. Topology Appl. 28, 277–287 (1988)
T. tom Dieck, Transformation Groups. de Gruyter Stud. Math. 8, Walter de Gruyter, Berlin, 1987.
Kosniowski C.: A note on RO(G)-graded G-bordism theory. Quart. J. Math. Oxford 26, 411–419 (1975)
Kosniowski C.: Equivariant stable homotopy and framed bordism. Trans. Amer. Math. Soc. 219, 225–234 (1976)
Koszul J.L.: Lectures on Groups of Transformations. Tata Institute of Fundamental Research, Bombay (1965)
J. Lee, Introduction to Topological Manifolds. 2nd ed., Grad. Texts Math. 202, Springer, New York, 2011.
J. P. May and S. R. Costenoble, Equivariant Homotopy and Cohomology Theory. CBMS Reg. Conf. Ser. Math. 91, Amer. Math. Soc., Providence, RI, 1996.
A. S. Mishchenko and Q. Morales Meléndez, Bordism of manifolds with proper action of a discrete group: Signatures and descriptions of G-bundles. arXiv:1112.2104 [math.AT], 2011.
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To Andrzej Granas with our respect and admiration
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Crabb, M.C., Mishchenko, A.S., Morales Meléndez, Q. et al. The Conner–Floyd bordism exact sequence—a new perspective. J. Fixed Point Theory Appl. 17, 253–273 (2015). https://doi.org/10.1007/s11784-015-0254-z
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DOI: https://doi.org/10.1007/s11784-015-0254-z