Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
brief category:people
-entry for hyperlinking references at conformal bootstrap
Sen’s conjecture (and a stub for D25-brane)
(to go with this physics.SE discussion)
Started arithmetic topology.
created a minimum at projective bundle
As written, I do not believe Theorem 4.1 is true. Certainly, the coreflection exists but it is unclear why the topology generated by the connected components of the open subsets of is in fact a locally connected space. It is only obvious that locally connected spaces are the fixed points of this construction. Either this case was being mistaken for the locally path-connected case or the mistake was made of assuming that connected subspaces of still need to be connected as subspaces of . Looking at the literature (Gleason’s paper “Universally locally connected refinements”) this simple refinement is used to show that the coreflection exists. However, the simple refinement and coreflection don’t seem to be the same. Rather, the coreflection is only guaranteed to be the infimum (in the lattice of topologies) of locally connected topologies larger than the topology of .
Jeremy Brazas
Someone anonymous has noted that the labels in two diagrams in triangle identities are misplaced. This seems clear. As the diagrams are external, can someone edit them who has access to the original code? There seem to be other errors (e.g. a C should be a D), as well.
added pointer to:
Also added more items under “Selected writings”
a bare list of references, to be !include
-ed in pertinent stand-alone entries, such as at complex oriented cohomology theory and at MΩΩSU(n)
wrote out parts of the proof of at Thom spectrum
Today I was asked for what I know about the development of the theory of Kan-fibrant simplicial manifolds. I realized that the nLab does not discuss this, so I have started a page now with the facts that come to mind right away. (Likely I forgot various things that should still be added.)
Expanded dinatural transformation a little with examples and references.
created stub for simplicial manifold
The conjecture is not true for all single-sorted algebraic theories and this was known by Soviet mathematicians. I added a short high-level explanation on this and some references to translated works that have more detail. Presumably one should edit rest of the page (and references to it) to make it clear throughout that (i) the conjecture is false (ii) the general question “Which algebraic categories have the Higman property?” is still interesting (and potentially something category-theorists could study).
started universal coefficient theorem
am giving this theorem its own stand-alone entry, for ease of hyperlinking between MUFr, Todd class and e-invariant.
At projective resolution I have
spelled out the Definition in lots of detail;
spelled out statement and proof of the existence of resolutions in full detail.
I am giving this its own little entry, for ease of collecting some facts and resources…
…such as the MO discussions (MO:a/44885/381, MO:a/218053/381) on how is the cobordism that witnesses . There must be a more citeable reference for this, though. If anyone has the pointer, let’s add it.
I have touched the Examples-section at sequentially compact topological space:
moved the detailed discussion of the compact space which is not sequ compact to the examples-section at compact topological space, and left a pointer to it,
added pointers (just pointers for the moment) to two detailed discussions of examples of sequ compact spaces that are not compact.
needed to be able to point to duality in physics, so I created an entry. For the moment just a glorified redirect.
brief category:people
-entry for hyperlinking references at Abrikosov vortex and vortex string
brief category:people
-entry for hyperlinking references at vortex string and at superconductor
some minimum on Nielsen-Olesen vortex strings (to go along the material at superconductor)
Under “Selected writings” I have added pointer to
and then I added quote of the following passage, from p. 11, on laying foundations for perturbative string theory via rigorous formulation of 2d SCFT in terms of conformal nets or similar:
I still have hopes, perhaps romantic ones, that string theory, or something inspired by it, will come back to life again. I believe it is interesting to attempt to formulate string theory in an “invariant” way, quite like it is useful to formulate geometry in a coordinate-independent way. One might, for example, start with a family , of hyperfinite type von Neumann algebras – to be a little technical – indexed by intervals of the circle with non-emptry complement (or of the super-circle). It may pay to formulate the starting point using the language of sheaves. This structure determines a braided monoidal C*-category with unit, …; briefly, a quantum theory. From a combination of such tensor categories (left and right movers) one would attempt to reconstruct (symmetries of) physical space-time. String amplitudes would correspond to arrows (intertwiners) of the tensor category. it would provide a general way of thinking about string theory that does not presuppose knowing the target space-time of the theory.
created a bare minimum at associative submanifold
just for completeness, to go along with cyclic group etc.
Our entries formal scheme and formal spectrum need attention. They fail to state their definitions clearly, and in parts to the extent that the main point is lost.
At formal scheme I have tried to clean up a bit right there in the Idea-section. But this needs to be expanded on.
What I really came for to this entry is that I wanted to make explicit the basic example which I now did add as
stub for generalized Calabi-Yau manifold, (for the moment just to record some references)
for completeness, to go alongside MUFr: The bordism theory of -structured manifolds with -structured boundaries, as per the last pages of Conner-Floyd 66 (not sure if there is any more recent account?!)
expanded E6 a bit.
brief category:people
-entry for hyperlinking references at Reissner-Nordström spacetime
am expanding the entry on smooth algebra (aka -rings, see the query box discussion there): more examples, more properties, etc.
But have to interrupt now.
I noticed that we are lacking C-infinity algebra, so I very briefly created a very stubby stub (no time right now…)