On Generalized Spaces which admit given Holonomy Groups.

Groups Which Do Not Admit Ghosts

A ghost in the stable module category of a group G is a map between representations of G that is invisible to Tate cohomology. We show that the only non-trivial finite p-groups whose stable module categories have no non-trivial ghosts are the cyclic groups C2 and C3. We compare this to the situation in the derived category of a commutative ring. We also determine for which groups G the second p...

Discrete Groups, Symmetric Spaces, and Global Holonomy

Holonomy Quantization of Moduli Spaces & Grothendieck Groups

Gelfand’s [1] charecterization of a topological space M by the duality relationship of M and A = F(M), the commutative algebra of functions on this space has deep implications including the development of spectral calculas by Connes [2].We investigate this scheme in this paper in the context of Monopole Moduli Space M using Seiberg-Witten Equations [3].A observation has been made here that the ...

Riemannian Twistor Spaces and Holonomy Groups

• The Penrose fibration CP 3 → HP 1 = S4 encodes a large part of the geometry of the 4-sphere. For instance, instanton solutions to the Yang-Mills equations on S4 pull back to holomorphic bundles on CP 3 [30]. This forms the basis of the Atiyah-Drinfeld-HitchinManin classification of the instantons [1]. Again, horizontal curves in CP 3 project onto branched minimal surfaces in S4. Using this Br...

Which Ambient Spaces Admit Isoperimetric Inequalities for Submanifolds?

We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities to hold.