Teruhisa Kadokami

Lens surgeries along the n-twisted Whitehead link

We determine lens surgeries (i.e.\ Dehn surgery yielding a lens space) along the

AMPHICHEIRAL LINKS WITH SPECIAL PROPERTIES, I

n

THE LINK-SYMMETRIC GROUPS OF 2-BRIDGE LINKS

-twisted Whitehead link. To do so, we first give necessary conditions to yield a lens space from the Alexander polynomial of the link as: (1)

DEHN SURGERY ALONG TORUS LINKS

n=1

IWASAWA TYPE FORMULA FOR COVERS OF A LINK IN A RATIONAL HOMOLOGY SPHERE

(i.e. the Whitehead link), and (2) one of surgery coefficients is 1, 2 or 3. Our interests are not only lens surgery itself but also how to apply the Alexander polynomial for this kind of problems.

An infinite family of prime knots with a certain property for the clasp number

We determine prime amphicheiral links with at least 2 components and up to 11 crossings. There are 27 such links. We check also special amphicheiralities. Most of prime links with up to 11 crossings are detected not to be amphicheiral by a condition on the Jones polynomial. For the rest links, we applied conditions from the Alexander polynomial. We added new necessary conditions for a special case.

On the Iwasawa invariants of a link in the 3-sphere

We describe the link-symmetric groups of 2-bridge links by Schuberts normal forms and Conways normal forms. The part of Schuberts normal forms is a collection of well-known facts. However, the part of Conways normal forms may be new. Moreover, we deal with Conways normal forms whose entries are even integers.

Seifert surgery on knots via Reidemeister torsion and Casson--Walker--Lescop invariant II

We determine Dehn surgery along torus links by using Rolfsen moves and the classification theorem of Seifert fibered spaces over S2.

Amphicheirality of links and Alexander invariants

Based on the analogy between links and primes, we present an analogue of the Iwasawas class number formula in a Zp-extension for the p-homology groups of pn-fold cyclic covers of a link in a rational homology 3-sphere. We also describe the associated Iwasawa invariants precisely for some examples and discuss analogies with the number field case.

Seifert surgery on knots via Reidemeister torsion and Casson–Walker–Lescop invariant

The clasp number