On the Brown-Peterson cohomology of BPU_n in lower dimensions and the Thom map

2020/05/06 by Xing Gu, Gu, Xing
Mathematics · #55N35 #55R35 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2005.03107

openalex publication_date 2020/05/06 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28

Abstract

For an odd prime p, we study the image of the Thom map from Brown-Peterson cohomology of BPU_n to the ordinary cohomology in dimensions 0≤ i≤ 2p+2, where BPU_n is the classifying space of the projective unitary group PU_n. Also we show that a family of well understood p-torsion cohomology classes y_p,k∈ H^2p^k+1+2(BPU_n;Z_(p)) are in the image of the Thom map.

Related

• The p-primary subgroups of the cohomology of BPU_n in dimensions less than 2p+5
• A formula for the mod p cohomology of BPU(p)
• The cohomology of the classifying space of PU(4)
• Operators on symmetric polynomials and applications in computing the cohomology of BPU_n
• On the p-primary subgroups of the cohomology of the classifying spaces of PUn