Related papers: On isotopy and unimodal inverse limit spaces

The aim of this note is to show that the automorphism and isometry groups of the C*-algebra $\l_\infty(N,B(H))$ of all bounded sequences in $B(H)$ are topologically reflexive which, as one of our former results shows, is not the case with…

The equivariant Gromov--Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dimension of the group guarantees that the convergence is by…

In this paper, we define certain symmetries for automorphic forms on O(2, m+2) and show that the space of automorphic forms satisfying these symmetries coincides with the Maass space, the image of Saito-Kurokawa lifting.

We establish an isomorphism of complex $K$-theory of the moduli space $\check{\mathcal{M}}$ of $``SL_n"$-Higgs bundles of degree $d$ and rank $n$ (in the sense of Hausel--Thaddeus) and twisted complex $K$-theory of the orbifold…

In this thesis, we prove several results concerning field-theoretic invariants of knots and 3-manifolds. In Chapter 2, for any knot $K$ in a closed, oriented 3-manifold $M$, we use $SU(2)$ representation spaces and the Lagrangian field…

Let $f$ be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric power lifting $\mathrm{Sym}^n f$ for every $n \geq 1$. We establish the same result for a more general class of cuspidal Hecke eigenforms, including…

We give another proof of a theorem of Scharlemann and Tomova and of a theorem of Hartshorn. The two theorems together say the following. Let M be a compact orientable irreducible 3--manifold and P a Heegaard surface of M. Suppose Q is…

We will prove that one-sided topological Markov shifts $(X_A,\sigma_A)$ and $(X_B,\sigma_B)$ for matrices $A$ and $B$ with entries in $\{0,1\}$ are topologically orbit equivalent if and only if there exists an isomorphism between the…

Various theorems on convergence of general space homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring $Q$--homeomorphisms are obtained. In particular, it was established by…

For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomorphisms, with…

We prove that for any nondegenerate dendrite $D$ there exist topologically mixing maps $F : D \to D$ and $f : [0, 1] \to [0, 1]$, such that the natural extensions (aka shift homeomorphisms) $\sigma_F$ and $\sigma_f$ are conjugate, and…

There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of…

Consider the infinite dimensional flag manifold $LK/T$ corresponding to the simple Lie group $K$ of rank $l$ and with maximal torus $T$. We show that, for $K$ of type $A$, $B$ or $C$, if we endow the space $H^*(LK/T)\otimes…

We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

We extend the unpublished work of M. Handel and R. Miller on the classification, up to isotopy, of endperiodic automorphisms of surfaces. We give the Handel-Miller construction of the geodesic laminations, give an axiomatic theory for…

We say that a space X admits a homology exponent if there exists an exponent for the torsion subgroup of the integral homology. Our main result states if an H-space of finite type admits a homology exponent, then either it is, up to…

Ishizaka classified up to conjugacy hyperelliptic periodic automorphisms of a surface. Here, an involution $I$ on a surface $\Sigma_{g}$ is hyperelliptic if and only if $\Sigma_{g}/\langle I \rangle$ is homeomorphic to $S^2$. In this…

We show that noncompact simply connected harmonic manifolds with volume density $\Theta_{p}(r) =\sinh ^{n-1} r$ is isometric to the real hyperbolic space and noncompact simply connected K\"{a}hler harmonic manifold with volume density…

We prove that for any infinite-type orientable surface S there exists a collection of essential curves {\Gamma} in S such that any homeomorphism that preserves the isotopy classes of the elements of {\Gamma} is isotopic to the identity. The…

For any homotopy class h in any compact orientable 3-manifold M which is closed or has exclusively torus boundary components, we produce infinitely many pairs of distinct knots representing h with orientation-preserving homeomorphic…