# Boston Graduate Topology Seminar

### Boston College Meeting

Saturday, February 22, 9:00AM-12:15PM

Math Department, Maloney Hall, Room 560

**Speakers:**

**9:30-10:15:** Inanc Baykur (UMass Amherst)

**Title:** Geography of surface bundles over surfaces

**Abstract: **An outstanding problem for surface bundles over surfaces, closely related to the symplectic geography problem in dimension four, is to determine for which fiber and base genera there are examples with non-zero signature. I will report on our recent progress (joint with Korkmaz), which resolves the question for all fiber and base genera except for about 20 pairs at the time of writing.

**10:30-11:15:** Corey Bregman (Brandeis)

**Title:** Surface bundles and algebraic geometry

**Abstract:** Kodaira, and independently Atiyah, provided the first examples of surface bundles over surfaces whose signature does not vanish. From a topological viewpoint, the Atiyah-Kodaira examples demonstrate that the signature of fiber bundles need not be multiplicative. However, their examples are in fact complex projective surfaces, admitting the structure of a holomorphic family of Riemann surfaces over a complex curve. We will review the construction of Atiyah and Kodaira before studying general Atiyah-Kodaira fibrations with nontrivial invariant cohomology. When the dimension of the invariants is at most two, we show that the total space admits a branched covering over a product of Riemann surfaces.

**11:30-12:15:** Mustafa Cengiz (BC)

**Title:** Heegaard genus and the complexity of fibered knots

**Abstract: **Translation distance is a measure of the complexity of a fibered knot/link. Saul Schleimer conjectured that for every three-manifold, there is a number that bounds the translation distance of any fibered knot in that manifold. By studying the interaction between Heegaard splittings and fibered knots, we confirm Schleimerâ€™s conjecture for fibered knots which do not induce minimal genus Heegaard splittings. More precisely, we show (1) any non-trivial fibered knot in the three-sphere has translation distance less than or equal 3, and (2) if a three-manifold M has Heegaard genus g greater than 0, then any fibered knot in M, which does not induce a minimal genus Heegaard splitting, has translation distance less than or equal 2g+2.

**Location & Parking:**

The Math Department is located on the fifth floor of Maloney Hall (shown on some campus maps as 21 Campanella Way), near the center of the main campus (shown in red on the map below). It is adjacent to the Commonwealth Garage. See this for more directions (including Public Transportation information) for getting to campus.

Visitor parking is available in the Commonwealth Garage or the Beacon Street Garage.