Quasipositive plumbing (constructions

of quasipositive knots and links, V)

Author:
Lee Rudolph

Journal:
Proc. Amer. Math. Soc. **126** (1998), 257-267

MSC (1991):
Primary 57M25; Secondary 32S55, 14H99

DOI:
https://doi.org/10.1090/S0002-9939-98-04407-4

MathSciNet review:
1452826

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Abstract | References | Similar Articles | Additional Information

Abstract: A Seifert surface is a *fiber surface* if a push-off induces a homotopy equivalence; roughly, is *quasipositive* if pushing into produces a piece of complex plane curve. A *Murasugi sum* (or *plumbing*) is a way to fit together two Seifert surfaces to build a new one. Gabai proved that a Murasugi sum is a fiber surface iff both its summands are; we prove the analogue for quasipositive Seifert surfaces. The *slice (or Murasugi) genus* of a link is the least genus of a smooth surface bounded by . By the local Thom Conjecture, if is quasipositive; we derive a lower bound for for any Seifert surface , in terms of quasipositive subsurfaces of .

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Additional Information

**Lee Rudolph**

Affiliation:
Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts 01610

Email:
lrudolph@black.clarku.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04407-4

Keywords:
Murasugi sum,
plumbing,
quasipositive,
slice genus,
Thom conjecture

Received by editor(s):
October 1, 1995

Additional Notes:
Partially supported by grants from CAICYT, NSF (DMS-8801915, DMS-9504832), and CNRS

Dedicated:
Dedicated to Professor Kunio Murasugi

Communicated by:
Ronald Stern

Article copyright:
© Copyright 1998
American Mathematical Society