Provider: JSTOR http://www.jstor.org Database: JSTOR Content: text/plain; charset="us-ascii" TY - CHAP TI - The formula for surgeries starting from rational homology spheres A2 - Lescop, Christine AB -

§4.2 to §4.5 prove the surgery formula T2 satisfied by λ, that is:

Proposition T2:

For any rational homology sphereM,and for any surgery presentationinM,the surgery formulaF(M,ℍ)is satisfied:$\text{(F(M,}\mathbb{H}\text{)) }\!\!\lambda\!\!\text{ (}{{\text{ }\!\!\chi\!\!\text{ }}_{\text{M}}}\text{(}\mathbb{H}\text{))=}\frac{\left| {{\text{H}}_{\text{1}}}\text{(}{{\text{ }\!\!\chi\!\!\text{ }}_{\text{M}}}\text{(}\mathbb{H}\text{))} \right|}{\left| {{\text{H}}_{\text{1}}}\text{(M)} \right|}\text{ }\!\!\lambda\!\!\text{ (M)+}{{\text{F}}_{\text{M}}}\text{(}\mathbb{H}\text{)}$

Section 4.7 relates the one-component surgery formula to the Walker formula, recalled in §4.6. This relationship implies that λ satisfies Property T5.0:

Property T5.0:

IfM isa rational homology sphere,and ifλwdenotes the Walker invariant as described in[W]:$\text{ }\!\!\lambda\!\!\text{ (M)=}\frac{\left| {{\text{H}}_{\text{1}}}\text{(M)} \right|}{\text{2}}{{\text{ }\!\!\lambda\!\!\text{ }}_{\text{W}}}\text{(M)}$

By definition, Proposition T2 holds for all surgery presentations in S3. Our approach to the proof of Proposition T2 will be to

EP - 80 PB - Princeton University Press PY - 1996 SN - 9780691021324 SP - 60 T2 - Global Surgery Formula for the Casson-Walker Invariant. (AM-140) UR - http://www.jstor.org/stable/j.ctt7zv8pj.6 Y2 - 2021/09/28/ ER -