Volume 11 (2007)

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Evens norm, transfers and characteristic classes for extraspecial p–groups

Pham Anh Minh

Geometry & Topology Monographs 11 (2007) 179–200

DOI: 10.2140/gtm.2007.11.179

arXiv: 0903.4973

Abstract

Let P be the extraspecial p–group of order p2n+1, of p–rank n + 1, and of exponent p if p > 2. Let Z be the center of P and let κn,r be the characteristic classes of degree 2n 2r (resp. 2(pn pr)) for p = 2 (resp. p > 2), 0 r n 1, of a degree pn faithful irreducible representation of P. It is known that, modulo nilradical, the ιth powers of the κn,r’s belong to T = Im(H(P∕Z,Fp)√ -
  0 Inf
− →H(P,Fp)√ -
  0), with ι = 1 if p = 2, ι = p if p > 2. We obtain formulae in H(P,Fp)√ -
  0 relating the κn,rι terms to the ones of fewer variables. For p > 2 and for a given sequence r0,,rn1 of non-negative integers, we also prove that, modulo-nilradical, the element riκn,iri belongs to T if and only if either r0 2, or all the ri are multiple of p. This gives the determination of the subring of invariants of the symplectic group Sp2n(Fp) in T .

Keywords

Extraspecial p–groups, Chern classes, Stiefiel–Whitney classes, Evens norm, transfer

Mathematical Subject Classification

Primary: 20J06

Secondary: 55S10

References
Publication

Received: 30 November 2004
Accepted: 23 January 2005

Authors
Pham Anh Minh
Department of Mathematics
College of Science
University of Hue
Dai hoc Khoa hoc
77 Nguyen Hue
Hue
Vietnam