seminars:topsem
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| * **October 30th** \\ Speaker: ** Tam Cheetham-West (Yale) ** \\ Title: ** Splittings and finite quotients of 3-manifold groups ** <WRAP box>// Abstract: // Embedded essential surfaces in a 3-manifold correspond to non-trivial splittings of its fundamental group. We give some conditions on the fundamental group of a Haken hyperbolic 3-manifold which guarantee that any other 3-manifold group with the same finite quotients must have a non-trivial splitting. Using one of these conditions, we obtain restrictions on the possible first Betti numbers of regular covers of aspherical integer homology spheres. This is joint work with Khánh Lê. \\ </WRAP> | * **October 30th** \\ Speaker: ** Tam Cheetham-West (Yale) ** \\ Title: ** Splittings and finite quotients of 3-manifold groups ** <WRAP box>// Abstract: // Embedded essential surfaces in a 3-manifold correspond to non-trivial splittings of its fundamental group. We give some conditions on the fundamental group of a Haken hyperbolic 3-manifold which guarantee that any other 3-manifold group with the same finite quotients must have a non-trivial splitting. Using one of these conditions, we obtain restrictions on the possible first Betti numbers of regular covers of aspherical integer homology spheres. This is joint work with Khánh Lê. \\ </WRAP> | ||
| - | * **November 6th** \\ Speaker: ** Genevieve Walsh (Tufts) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **November 6th** \\ Speaker: ** Genevieve Walsh (Tufts) ** \\ Title: ** Hyperbolic groups vs relatively hyperbolic groups** <WRAP box>// Abstract: // A hyperbolic group is a group that acts geometrically on a hyperbolic |
| + | metric space, and a relatively hyperbolic group is a group that acts | ||
| + | geometrically finitely on a hyperbolic metric space. | ||
| + | Sometimes, these spaces are quasi-isometric. This turns out to be | ||
| + | exceedingly rare. We will discuss the consequences of such | ||
| + | quasi-isometries, and give lots of examples of these types of group | ||
| + | actions. This is joint work with Emily Stark. \\ </WRAP> | ||
| - | * **November 13th** \\ Speaker: ** Maximilien Peroux (Michigan State University) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **November 13th** \\ Speaker: ** Maximilien Peroux (Michigan State University) ** \\ Title: ** Algebraic characterization of cobordism theories ** <WRAP box>// Abstract: // Cobordism theories are fundamental invariants in geometry and topology: they organize closed manifolds according to whether or not they bound. They play a central role in classification problems and have deep connections to index theory, characteristic classes, and even modern mathematical physics. Each variant of cobordism is represented in stable homotopy theory by a Thom spectrum, linking geometric questions with homotopical constructions. Recognizing which spectra arise as Thom spectra is a subtle problem, since it amounts to detecting when an abstract homotopy-theoretic object has a geometric origin in cobordism. |
| + | In ongoing joint work with Brazelton, Calle, Chan, and Keenan, we introduce an algebraic characterization of Thom spectra as certain algebraic objects in stable homotopy theory. This approach provides a new algebraic perspective on geometric phenomena. \\ </WRAP> | ||
| - | * **November 20th** \\ Speaker: ** David Chan (Michigan State University) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **November 20th** \\ Speaker: ** David Chan (Michigan State University) ** \\ Title: ** Building equivariant infinite loop spaces ** <WRAP box>// Abstract: // Infinite loop spaces are important kinds of topological spaces which can be used to construct cohomology theories. For a finite group G, there is an equivariant refinement of infinite loop spaces which represent cohomology theories for G-spaces. Infinite loop G-spaces play an important role in recent applications of equivariant homotopy theory, but constructing examples can be difficult. In this talk we will describe some results about how to construct every possible infinite loop G-space from algebraic input. |
| + | \\ </WRAP> | ||
| * **November 27th** \\ No seminar \\ | * **November 27th** \\ No seminar \\ | ||
| - | * **December 4th** \\ Speaker: **Hongbin Sun (Rutgers) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **December 4th** \\ Speaker: **Hongbin Sun (Rutgers) ** \\ Title: ** On virtual chirality of 3-manifolds ** <WRAP box>// Abstract: // We prove that if a prime 3-manifold M is not finitely covered by the 3-sphere or a product manifold, then M is virtually chiral, i.e. it has a finite cover that does not admit an orientation-reversing self-homeomorphism. For a non-prime 3-manifold, it is virtually chiral if it has a virtually chiral prime summand. This is joint work with Zhongzi Wang. \\ </WRAP> |
seminars/topsem.1761252041.txt · Last modified: 2025/10/23 16:40 by lruffoni