pilemma · PSEUDO-ORGANIZED MATHEMATICAL ANTIQUES · soft opening

The Manifold Curiosity Shop

An antique shop of topology in the old town.
Stocked through 2020. Bring numbers, group symbols, decimals, or a half-remembered sequence. Strong matches stay on parchment; loose coincidences are pushed into the dark-brown bargain drawer and must confess exactly what matched.
MATH AUDIT · homology/UCT/Künneth checked against Hatcher · 4D claims checked against Manolescu/primary references · knot fingerprints normalized conservatively
STOCKED thru 2020 FINITE COLLECTION Not all INSPECTED
shelf masks L0 on sale · L1 old favorites · L2 troublemakers · L3 workshop · L4 new acquisitions
how to look
rooms
firepower
token lottery
No arithmetic matching. “Suspicion” is a curiosity meter, not a probability. For multi-token queries, a one-token collision never becomes a real lead. At most, a dark-brown drawer murmurs and tells you exactly what it heard. O### opens old stock; E### opens the exotica index; F### opens 4-manifold files. These are shop filing codes, not mathematical invariants.
shop status
The drawers are closed.
Try something you vaguely remember, or buy a ticket in the Token Lottery.
the counter

Put an object down. Then take it somewhere.

The counter is one room with several specialist desks. Manifolds can be combined or sent to topology desks; knots keep their own operations and paperwork. A transformed object can come back to the counter and visit a different desk.
object table

What are you bringing in?

manifolds
knots
on the counter
available operations

What can happen on the counter?

take it to a desk

Who should look at it?

homology desk

H_* / H^*

quiet
Shop policy: when a standard machine explains the calculation, the clerk may recommend the theorem card first. You can still ask to see the groups.
curated homotopy lookup

Lookup shelf, not a fake universal calculator.

quiet
Recognized shelf names: S¹–S⁸ through π₁₂ · stable stems 0–19 · Tⁿ · L(p,q) · CP∞ · RP∞ · K3 · Poincaré · finite products. Some names are “pseudo-stock”: the desk recognizes the object but may route a missing group to a theorem card or simply say Not stocked.
Policy: finite stock on purpose. A few drawers in the stocked range are deliberately left empty and point to the Theorem Cabinet so you can calculate them yourself.
Tap an example to load it:
knot desk

Polynomials, Floer fingerprints, and other knot paperwork.

quiet
4D intersection-form / Kirby desk

Middle-dimensional forms for closed oriented 4-manifolds.

quiet
Here “intersection form” means the symmetric pairing on H₂ of a closed oriented 4-manifold. Surfaces have an H₁ intersection pairing too, but that one is skew-symmetric and does not belong on this desk.
form blocks · orthogonal sum
These are LEGO pieces for an abstract symmetric bilinear form, not manifold buttons. Add blocks to build Q = Q₁ ⊕ Q₂ ⊕ ···. If the current 4-manifold has a stocked decomposition, you can load it here.
no form blocks yet
paste / edit a symmetric matrix
Seiberg–Witten shelf

A small gauge-theory shelf.

quiet
K3 = E(2)
only basic class 0, |SW|=1.
blow-up
K becomes K±E.
connected sum
positive b₂⁺ on both sides ⇒ ordinary SW vanishes.
knot surgery
Alexander polynomial enters the SW fingerprint.
the easel

What should I put on the easel?

This is deliberately not a difficulty ranking. “Challenge” often means the mathematics is hard to depict honestly, which is exactly why it may be a good illustration problem.
filter
linear era map

One very selective topology timeline.

office
small notice

WE ALSO BUY ANTIQUES

Found an old manifold, knot, invariant, counterexample, or suspicious sequence? The shop may be interested.

Contact the owner on February 30, April 31, June 31, September 31, or November 31.

hiring

ANTIQUE APPRAISER

Identifying suspicious mathematical objects · checking provenance · detecting fake folklore · distinguishing homeomorphic from diffeomorphic merchandise · recognizing when identical-looking knots are, unfortunately, not the same knot.

Experience with dusty textbooks preferred. No prior retail experience required.