J connects prepositions to their objects.
+-Mp+----J---+ +-----MVp----+-J-+
| | | | | |
The man with the hat chased the dog on Tuesday
Proper and common nouns, accusative pronouns, and other words
that can act as noun-phrases have J- disjoined with their
S+,
SI-, and
O- connectors.
Prepositions have "J+ & (Mp- or MVp-)". Mp is used for prepositions modifying nouns; MVp is used for prepositions modifying verbs and adjectives. Prepositions may also have other connectors, disjoined with J+, such as Mg+, Mv+, and QI+; see "MV: Other Uses of MVp and MVs".
+----------Op---------+
| +----Dmc----+
| +--Ds-+-OFd-+--Jd-+
| | | | |
I have.v a number.d of cookies.n
In the above example "a number of" is acting effectively as
a determiner phrase. Thus, its head word, "number", gets a D+
link. Yet, the phrase ends with a preposition that shouldn't dangle,
and so, for this case, a Jd+ link is also used to complete
the loop. Plural and mass nouns have a
(Jd- & D- & O-) disjunct on them.
+-------I-------+
| +--VJlpi--+-----------Jk----------+
| +-MVp+-Jj-+--VJrpi-+--MVp-+---Js--+
| | | | | | |
... to.r look.v at and.j-v listen.v to.r everything
Here, the Jj and Jk should be taken as artificially
forming a single link, that crosses over the conjunction, and indicates
that the prepositional object of "at" is "everything". (Paraphrasing,
"... to look at everything and listen to everything.") In this example,
there is no way to create a single Js link from "at" to
"everything" without voilating planarity. Thus, planarity is maintained
by splitting Js into two, with the split being a "hole" or
"jump", allowing limited non-planarity. Thus, Jj and Jk
can be thought of as forming a single link, with a "hole" in it, with
that hole being exactly the right shape to hop over the conjunction.