2,955 research outputs found
The canonical pencils on Horikawa surfaces
We calculate the monodromies of the canonical Lefschetz pencils on a pair of
homeomorphic Horikawa surfaces. We show in particular that the (pluri)canonical
pencils on these surfaces have the same monodromy groups, and are related by a
"partial twisting" operation.Comment: This is the version published by Geometry & Topology on 29 November
200
Enumerative geometry via the moduli space of super Riemann surfaces
In this paper we relate volumes of moduli spaces of super Riemann surfaces to
integrals over the moduli space of stable Riemann surfaces . This allows us to use a recursion between the super volumes recently
proven by Stanford and Witten to deduce recursion relations of a natural
collection of cohomology classes . We give a new proof that a generating function for the intersection
numbers of with tautological classes on is a KdV tau function. This is an analogue of the Kontsevich-Witten
theorem where is replaced by the unit class . The proof is analogous to Mirzakhani's proof of
the Kontsevich-Witten theorem replacing volumes of moduli spaces of hyperbolic
surfaces with volumes of moduli spaces of super hyperbolic surfaces.Comment: 65 page
The braided Ptolemy-Thompson group is finitely presented
Pursueing our investigations on the relations between Thompson groups and
mapping class groups, we introduce the group (and its further
generalizations) which is an extension of the Ptolemy-Thompson group by
means of the full braid group on infinitely many strands. We prove
that it is a finitely presented group with solvable word problem, and give an
explicit presentation of it.Comment: 35
From braid groups to mapping class groups
This paper is a survey of some properties of the braid groups and related
groups that lead to questions on mapping class groups
Integration and conjugacy in knot theory
This thesis consists of three self-contained chapters. The first two concern
quantum invariants of links and three manifolds and the third contains results
on the word problem for link groups.
In chapter 1 we relate the tree part of the Aarhus integral to the
mu-invariants of string-links in homology balls thus generalizing results of
Habegger and Masbaum.
There is a folklore result in physics saying that the Feynman integration of
an exponential is itself an exponential. In chapter 2 we state and prove an
exact formulation of this statement in the language which is used in the theory
of finite type invariants.
The final chapter is concerned with properties of link groups. In particular
we study the relationship between known solutions from small cancellation
theory and normal surface theory for the word and conjugacy problems of the
groups of (prime) alternating links. We show that two of the algorithms in the
literature for solving the word problem, each using one of the two approaches,
are the same. Then, by considering small cancellation methods, we give a normal
surface solution to the conjugacy problem of these link groups and characterize
the conjugacy classes. Finally as an application of the small cancellation
properties of link groups we give a new proof that alternating links are
non-trivial.Comment: University of Warwick Ph.D. thesi
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