Acta mathematica scientia, Series B >
INVOLUTIONS FIXING ∪mi=1CPi(1) ×|HPi(n)
Received date: 2010-05-31
Online published: 2012-05-20
Supported by
This work is supported by NSFC (10971050; 11001073; 10901045), HNSFC(A2010000828), and FHUST (XL201043; QD201021).
Let (M, T) be a closed manifold with an involution T. The fixed point set of T is F. In this article, bordism classes of the involutions with fixed point set F =∪mi=1CPi(1) × HPi(n) are determined, where CP(1) and HP(n) denote the 1-dimensional complex projective space and n-dimensional quaternionic projective space respectively, and n = 2p− 2 or n = 2p− 1 (p > 1).
Key words： Involution; bordism; fixed point set; Stiefel-Whitney class
ZHAO Su-Qian , WANG Yan-Ying . INVOLUTIONS FIXING ∪mi=1CPi(1) ×|HPi(n)[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 1021 -1034 . DOI: 10.1016/S0252-9602(12)60076-9
[1] Royster D C. Involutions fixing the disjoint union of two projective spaces. Indiana Univ Math J, 1980, 29: 267–276
[2] Hou D, Torrence B. Involutions fixing the disjoint union of odd-dimensional projective spaces. Canad Math Bull, 1994, 37: 66–74
[3] Hou D, Torrence B. Involutions fixing the disjoint union of copies of even projective spaces. Acta Math Sin (Engl Ser), 1996, 12: 162–166
[4] Stong R E. Involutions fixing products of circles. Proc Amer Math Soc, 1993, 119: 1005–1008
[5] Ding Y H, Liu Z Z. Involutions fixing products of projective spaces. Northeast Math J, 1999, 15: 97–102
[6] Ma K, Liu Z Z. Involution fixing ∪ri=1(RP(1))mi × (CP(1))si . Northeast Math J, 1999, 15: 46–52
[7] Li J Y, Wang Y Y. Characteristic classes of vector bundles over RP(h) × HP(k). Topology Appl, 2007, 154: 1778–1793
[8] Singmaster D. Notes on binomial coefficients. J Lond Math Soc, 1974, 8: 545–560
[9] Steenrod N E, Epstein B A. Cohomology Operations. Princeton, New Jersey: Princeton Univ Press, 1962
[10] Milnor J W, Stasheff J D. Characteristic Classes. Princeton, New Jersey: Princeton Univ Press and Univ of Tokyo Press, 1974
[11] Kosniowski C, Stong R E. Involutions and characteristic numbers. Topology, 1978, 17: 309–330
[12] Conner P E. Differentiable periodic maps//Dold A, Eckmann B. Lecture Notes in Math 738. Second Edition. Berlin: Springer-Verlag, 1979
/
| 〈 |
|
〉 |