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Small 3manifolds of large genus
"... Abstract. We prove the existence of pure braids with arbitrarily many strands which are small, i.e. they contain no closed incompressible surface in the complement which is not boundary parallel. This implies the existence of irreducible nonHaken 3manifolds of arbitrarily high Heegaard genus. 1. ..."
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Cited by 7 (0 self)
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Abstract. We prove the existence of pure braids with arbitrarily many strands which are small, i.e. they contain no closed incompressible surface in the complement which is not boundary parallel. This implies the existence of irreducible nonHaken 3manifolds of arbitrarily high Heegaard genus. 1.
Wildly ramified covers with large genus
, 2005
"... We study wildly ramified GGalois covers φ: Y → X branched at B (defined over an algebraically closed field of characteristic p). We show that curves Y of arbitrarily high genus occur for such covers even when G, X, B and the inertia groups are fixed. The proof relies on a Galois action on covers of ..."
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We study wildly ramified GGalois covers φ: Y → X branched at B (defined over an algebraically closed field of characteristic p). We show that curves Y of arbitrarily high genus occur for such covers even when G, X, B and the inertia groups are fixed. The proof relies on a Galois action on covers
ON THE LARGE GENUS ASYMPTOTICS OF WEILPETERSSON VOLUMES
, 2008
"... Abstract. A relatively fast algorithm for evaluating WeilPetersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of the WeilPetersson volumes is computed. Asymptotic formulas for the intersection numbers invo ..."
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Cited by 7 (1 self)
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Abstract. A relatively fast algorithm for evaluating WeilPetersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of the WeilPetersson volumes is computed. Asymptotic formulas for the intersection numbers
Computing discrete logarithms in real quadratic congruence function fields of large genus
 Math. Comp
, 1999
"... Abstract. The discrete logarithm problem in various finite abelian groups is the basis for some well known public key cryptosystems. Recently, real quadratic congruence function fields were used to construct a public key distribution system. The security of this public key system is based on the dif ..."
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Cited by 39 (9 self)
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on the difficulty of a discrete logarithm problem in these fields. In this paper, we present a probabilistic algorithm with subexponential running time that computes such discrete logarithms in real quadratic congruence function fields of sufficiently large genus. This algorithm is a generalization of similar
THE LARGE GENUS LIMIT OF THE INFIMUM OF THE WILLMORE ENERGY
"... Abstract. The Willmore energy of a surface immersed into R n is the integral of its squared mean curvature. It is known that the infimum β n p of the Willmore energy among all closed oriented surfaces of genus p in R n is attained by a smooth embedded surface, and that 4π <β n p < 8π for p ≥ 1 ..."
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Cited by 10 (2 self)
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Abstract. The Willmore energy of a surface immersed into R n is the integral of its squared mean curvature. It is known that the infimum β n p of the Willmore energy among all closed oriented surfaces of genus p in R n is attained by a smooth embedded surface, and that 4π <β n p < 8π for p
THE MODULI SPACE OF RIEMANN SURFACES OF LARGE GENUS
"... Abstract. LetMg, be the thick part of the moduli spaceMg of closed genus g surfaces. In this article, we show that the number of balls of radius r needed to coverMg, is bounded below by (c1g)2g and bounded above by (c2g)2g, where the constants c1, c2 depend only on and r, and in particular not o ..."
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Abstract. LetMg, be the thick part of the moduli spaceMg of closed genus g surfaces. In this article, we show that the number of balls of radius r needed to coverMg, is bounded below by (c1g)2g and bounded above by (c2g)2g, where the constants c1, c2 depend only on and r, and in particular
Split States, Entropy Enigmas, Holes and Halos
, 2007
"... We investigate degeneracies of BPS states of Dbranes on compact CalabiYau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute e ..."
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Cited by 235 (22 self)
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explicitly exact indices of various nontrivial Dbrane systems, and to clarify the subtle relation of DonaldsonThomas invariants to BPS indices of stable D6D2D0 states, realized in supergravity as “hole halos. ” We introduce a convergent generating function for D4 indices in the large CY volume limit
Genus
, 1998
"... statistics on CMB polarization maps and cosmological parameter degeneracy ..."
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statistics on CMB polarization maps and cosmological parameter degeneracy
Results 1  10
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149,559