arXiv subjects
Publications and source records attributed to Po Hu.
For a compact simply connected simple Lie group $G$ with an involution $α$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\Z/2$ acts either by $α$ or by $g\mapsto α(g)^{-1}$. We also give a representation-theoretic interpretation of those groups, as well as of $K_G(G)$.
Extending our method for investigating Real cobordism (which was recently used by Hill, Hopkins and Ravenel in their solution of the Kervaire invariant 1 problem), we investigate the $RO(G)$-graded homotopy groups of a (non-complete) $\Z/2\times \Z/2$-equivariant spectrum called topological Hermitian cobordism. The methods of this paper may be useful in computing the homotopy groups of other $G$-equivariant spectra where $G\neq \Z/2$.
We define a general concept of pseudo algebras over theories and 2-theories. A more restrictive such notion was introduced by Hu and Kriz, but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the mistake by introducing a more general concept, allowing more flexibility in selecting coherence diagrams for pseudo algebras.
In this note, we define the notion of a cactus set, and show that its geometric realization is naturally an algebra over Voronov's cactus operad, which is equivalent to the framed 2-dimensional little disks operad $\mathcal{D}_2$. Using this, we show that the Hochschild cohomology of a Poincaré algebra A is an algebra over (the chain complexes of) $\mathcal{D}_2$.
In this note, we calculate all untwisted and twisted (Z/2)^n-equivariant K-groups with compact supports of real finite-dimensional linear representations of (Z/2)^n. The question was motivated by the question of D-brane charges for orbifold type II string vacua.
In this paper, we show how to adapt our rigorous mathematical formalism for closed/open conformal field theory so that it captures the known physical theory of branes in the WZW model. This includes a mathematically precise approach to the Kondo effect, which is an example of evolution of one conformally invariant boundary condition into another through boundary conditions which can break conformal invariance, and a proposed mathematical statement of the Kondo effect conjecture. We also review some of the known physical results on WZW boundary conditions from a mathematical perspective.
In this paper, we give a general axiomatization of anomalies in closed and open conformal field theories. In particular, we generalize Segal's notion of modular functor to a setting where the ``set of labels'' is a 2-vector space. In the case of open conformal field theory, the ``set of $D$-branes'' is a 3-vector space. We also define a ``topological group completion'' of the symmetric bimonoidal category of finite-dimensional vector spaces, and propose it as a candidate for labelling conformal field theories whose modular functors are super-vector spaces.
Answering a question of W. S. Wilson, I introduce a Z/2-equivariant Atiyah-Real analogue of Johnson-Wilson cohomology theory BP , whose coefficient ring is the =< n-chromatic part of Landweber's Real cobordism ring.