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pro vyhledávání: '"55R35, 55R40"'
Let $PU_n$ the projective unitary group of rank $n$ and $BPU_n$ its classifying space. For an odd prime $p$, we extend previous results to a compete description of $H^s(BPU_n;\mathbb{Z})_{(p)}$ for $s<2p+5$ by showing that the $p$-primary subgroups o
Externí odkaz:
http://arxiv.org/abs/2108.03571
Autor:
Crowley, Diarmuid, Gu, Xing
For the projective unitary group $PU_n$ with a maximal torus $T_{PU_n}$ and Weyl group $W$, we show that the integral restriction homomorphism \[\rho_{PU_n} \colon H^*(BPU_n;\mathbb{Z})\rightarrow H^*(BT_{PU_n};\mathbb{Z})^W\] to the integral invaria
Externí odkaz:
http://arxiv.org/abs/2103.03523
Autor:
Gu, Xing
We determine a subring of the Chow ring and the cohomology of $BPGL_n$, the classifying space of the projective linear group of degree $n$ over complex numbers, and explain a way in which this computation might play a role in the period-index problem
Externí odkaz:
http://arxiv.org/abs/2012.00199
Autor:
Bianchi, Andrea
Publikováno v:
Journal of Topology 13:3 (2020) 1230-1260
Let $\Gamma_{g,1}^m$ be the mapping class group of the orientable surface $\Sigma_{g,1}^m$ of genus $g$ with one parametrised boundary curve and $m$ permutable punctures; when $m=0$ we omit it from the notation. Let $\beta_{m}(\Sigma_{g,1})$ be the b
Externí odkaz:
http://arxiv.org/abs/1903.06065
Autor:
Gu, Xing
Publikováno v:
J London Math Soc, 103(1), 2021
In the integral cohomology ring of the classifying space of the projective linear group $PGL_n$ (over $\mathbb{C}$), we find a collection of $p$-torsions $y_{p,k}$ of degree $2(p^{k+1}+1)$ for any odd prime divisor $p$ of $n$, and $k\geq 0$. If in ad
Externí odkaz:
http://arxiv.org/abs/1901.10090
Autor:
Gu, Xing
Let $\mathbf{B}PU_{n}$ be the classifying space of $PU_n$, the projective unitary group of order $n$, for $n>1$. We use the Serre spectral sequence associated to a fiber sequence $\mathbf{B}U_n\rightarrow\mathbf{B}PU_n\rightarrow K(\mathbb{Z},3)$ to
Externí odkaz:
http://arxiv.org/abs/1612.00506
In this paper we present new examples of simple $p$-local compact groups for all odd primes. We also develop the necessary tools to show saturation, simpleness and the non-realizability as $p$-compact groups or compact Lie groups, which can be applie
Externí odkaz:
http://arxiv.org/abs/1512.00284
Autor:
Gonzalez, Alex
Publikováno v:
Geom. Topol. 20 (2016) 2923-2995
We show that the classifying space of a $p$-local compact group is approximated by a telescope of classifying spaces of $p$-local finite groups. This result has numerous implications, like a Stable Elements Theorem for $p$-local compact groups, or th
Externí odkaz:
http://arxiv.org/abs/1503.08856
Autor:
Díaz, Antonio, Park, Sejong
We extend Dwyer's sharp subgroup homology decomposition of the classifying space of a finite group to arbitrary saturated fusion systems and arbitrary Mackey functors.
Comment: The proof of the main result (Theorem 1.3) is not complete as there
Comment: The proof of the main result (Theorem 1.3) is not complete as there
Externí odkaz:
http://arxiv.org/abs/1412.0378
Publikováno v:
Algebr. Geom. Topol. 14 (2014) 1181-1204
The most basic characteristic classes of smooth fibre bundles are the generalised Miller-Morita-Mumford classes, obtained by fibre integrating characteristic classes of the vertical tangent bundle. In this note we show that they may be defined for mo
Externí odkaz:
http://arxiv.org/abs/1306.3332