8 papers
'Topological parallel world' constructed by modification of space-time along observables
Eiji Ogasa
We introduce a new concept, `(topological) (vacuum) parallel world, ' which is a new tool to research submanifolds. Roughly speaking, `Observables in (T)QFT' is equal to `a (topolo…
Ribbon-moves of 2-knots: the torsion linking pairing and the -invariants of 2-knots
Eiji Ogasa
We discuss the ribbon-move for 2-knots, which is a local move. Let and be 2-knots. Then we have: Suppose that and are ribbon-move equivalent. (1) Let ${\mathrm {T…
Remarks on -dimensional Feynman diagrams, for example, which will appear in M-theory and in F-theory
Eiji Ogasa
We state some remarks on `-dimensional Feynman diagrams' (). There are different features between in the case of -dimensional Feynman diagrams() and in the 1…
n-dimensional links, their components, and their band-sums
Eiji Ogasa
We prove the following results (1) (2) (3) on relations between -links and their components. (1) Let L=(L_1, L_2) be a (4k+1)-link (4k+1\geq 5). Then we have Arf L=Arf L_1+Arf L…
Ribbon-moves of 2-links preserve the μ-invariant of 2-links
Eiji Ogasa
We introduce ribbon-moves of 2-knots, which are operations to make 2-knots into new 2-knots by local operations in B^4. (We do not assume the new knots is not equivalent to the old…
Ribbon-moves of 2-knots: the Farber-Levine pairing and the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman -invariants of 2-knots
Eiji Ogasa
Let K and K' be 2-knots. Suppose that K and K' are ribbon-move equivalent. Then the Farber-Levine pairing for K is equivalent to that for K' and the (Z-)torsion part of the first A…